(BQ) Part 2 book Business statistics in practice has contents: Comparing two means and two proportions, statistical inferences for population variances, experimental design and analysis of variance, simple linear regression analysis, multiple regression and model building, time series forecasting and index numbers,...and other contents.
bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 380 CHAPTER 10 www.downloadslide.com Comparing Two Means and Two Proportions Learning Objectives After mastering the material in this chapter, you will be able to: LO10-1 Compare two population means when the samples are independent LO10-2 Recognize when data come from independent samples and when they are paired Chapter Outline 10.1 Comparing Two Population Means by Using Independent Samples 10.2 Paired Difference Experiments LO10-3 Compare two population means when the data are paired LO10-4 Compare two population proportions using large independent samples 10.3 Comparing Two Population Proportions by Using Large, Independent Samples bow21493_ch10_380-411.qxd 12/3/12 11:53 AM Page 381 www.downloadslide.com B population means and two population proportions We make these comparisons by studying differences For instance, to compare two population means, say m1 and m2, we consider the difference between these means, m1 Ϫ m2 If, for example, we use a confidence interval or hypothesis test to conclude that m1 Ϫ m2 is a positive number, then we conclude that m1 is greater than m2 On the other hand, if a confidence interval or hypothesis test shows that m1 Ϫ m2 is a negative number, then we conclude that m1 is less than m2 We explain many of this chapter’s methods in the context of three new cases: usiness improvement often requires making comparisons For example, to increase consumer awareness of a product or service, it might be necessary to compare different types of advertising campaigns Or to offer more profitable investments to its customers, an investment firm might compare the profitability of different investment portfolios As a third example, a manufacturer might compare different production methods in order to minimize or eliminate out-ofspecification product In this chapter we discuss using confidence intervals and hypothesis tests to compare two populations Specifically, we compare two C The Catalyst Comparison Case: The production supervisor at a chemical plant uses confidence intervals and hypothesis tests for the difference between two population means to determine which of two catalysts maximizes the hourly yield of a chemical process By maximizing yield, the plant increases its productivity and improves its profitability The Auto Insurance Case: In order to reduce the costs of automobile accident claims, an insurance company uses confidence intervals and hypothesis tests for the difference between two population means to compare repair cost estimates for damaged cars at two different garages The Test Market Case: An advertising agency is test marketing a new product by using one advertising campaign in Des Moines, Iowa, and a different campaign in Toledo, Ohio The agency uses confidence intervals and hypothesis tests for the difference between two population proportions to compare the effectiveness of the two advertising campaigns 10.1 Comparing Two Population Means by Using Independent Samples A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours We let m1 denote the population mean customer waiting time during peak business hours under the current system To estimate m1, the manager randomly selects n1 ϭ 100 customers and records the length of time each customer spends waiting for service The manager finds that the mean and the variance of the waiting times for these 100 customers are x ϭ 8.79 minutes and s21 ϭ 4.8237 We let m2 denote the population mean customer waiting time during peak business hours for the new system During a trial run, the manager finds that the mean and the variance of the waiting times for a random sample of n2 ϭ 100 customers are x2 ϭ 5.14 minutes and s22 ϭ 1.7927 In order to compare m1 and m2, the manager estimates m1 Ϫ m2, the difference between m1 and m2 Intuitively, a logical point estimate of m1 Ϫ m2 is the difference between the sample means x Ϫ x ϭ 8.79 Ϫ 5.14 ϭ 3.65 minutes This says we estimate that the current population mean waiting time is 3.65 minutes longer than the population mean waiting time under the new system That is, we estimate that the new system reduces the mean waiting time by 3.65 minutes To compute a confidence interval for m1 Ϫ m2 (or to test a hypothesis about m1 Ϫ m2), we need to know the properties of the sampling distribution of x Ϫ x To understand this sampling distribution, consider randomly selecting a sample1 of n1 measurements from a population having mean m1 and variance s21 Let x be the mean of this sample Also consider randomly selecting a Each sample in this chapter is a random sample As has been our practice throughout this book, for brevity we sometimes refer to “random samples” as “samples.” LO10-1 Compare two population means when the samples are independent bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 382 www.downloadslide.com 382 Chapter 10 FIGURE 10.1 Comparing Two Means and Two Proportions The Sampling Distribution of x1 ؊ x2 Has Mean M1 ؊ M2 and Standard Deviation Sx1Ϫ x2 x1 Ϫ x2 1 Ϫ 2 x Ϫ x2 ϭ 21 n1 ϩ 22 n2 sample of n2 measurements from another population having mean m2 and variance s22 Let x be the mean of this sample Different samples from the first population would give different values of x 1, and different samples from the second population would give different values of x 2—so different pairs of samples from the two populations would give different values of x Ϫ x In the following box we describe the sampling distribution of x ؊ x 2, which is the probability distribution of all possible values of x Ϫ x Here we assume that the randomly selected samples from the two populations are independent of each other This means that there is no relationship between the measurements in one sample and the measurements in the other sample In such a case, we say that we are performing an independent samples experiment The Sampling Distribution of x1 ؊ x2 I f the randomly selected samples are independent of each other, then the population of all possible values of x1 Ϫ x2 Has a normal distribution if each sampled population has a normal distribution, or has approximately a normal distribution if the sampled populations are not normally distributed and each of the sample sizes n1 and n2 is large Has mean mx1Ϫ x2 ϭ m1 Ϫ m2 Has standard deviation sx1 Ϫ x2 ϭ s21 s22 ϩ n2 B n1 Figure 10.1 illustrates the sampling distribution of x Ϫ x Using this sampling distribution, we can find a confidence interval for and test a hypothesis about m1 Ϫ m2 by using the normal distribution However, the interval and test assume that the true values of the population variances s21 and s22 are known, which is very unlikely Therefore, we will estimate s21 and s22 by using s21 and s22, the variances of the samples randomly selected from the populations being compared, and base a confidence interval and a hypothesis test on the t distribution There are two approaches to doing this The first approach gives theoretically correct confidence intervals and hypothesis tests but assumes that the population variances s21 and s22 are equal The second approach does not require that s21 and s22 are equal but gives only approximately correct confidence intervals and hypothesis tests In the bank customer waiting time situation, the sample variances are s21 ϭ 4.8237 and s22 ϭ 1.7927 The difference in these sample variances makes it questionable to assume that the population variances are equal More will be said later about deciding whether we can assume that two population variances are equal and about choosing bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 383 www.downloadslide.com 10.1 Comparing Two Population Means by Using Independent Samples 383 between the two t-distribution approaches in a particular situation For now, we will first consider the case where the population variances s21 and s22 can be assumed to be equal Denoting the common value of these variances as s2, it follows that sx1Ϫx2 ϭ s21 s2 s2 s2 1 ϩ 2ϭ ϩ ϭ s2 ϩ B n1 n2 B n1 n2 B n1 n2 Because we are assuming that s21 ϭ s22 ϭ s , we not need separate estimates of s21 and s22 Instead, we combine the results of the two independent random samples to compute a single estimate of s2 This estimate is called the pooled estimate of s2, and it is a weighted average of the two sample variances s21 and s22 Denoting the pooled estimate as s2p, it is computed using the formula s2p ϭ (n Ϫ 1)s21 ϩ (n Ϫ 1)s22 n1 ϩ n2 Ϫ Using s2p, the estimate of sx1Ϫx2 is B s2p n ϩ 1 n2 and we form the statistic ( x Ϫ x 2) Ϫ (m1 Ϫ m 2) B s2p n ϩ 1 n2 It can be shown that, if we have randomly selected independent samples from two normally distributed populations having equal variances, then the sampling distribution of this statistic is a t distribution having (n1 ϩ n2 Ϫ 2) degrees of freedom Therefore, we can obtain the following confidence interval for m1 Ϫ m2: A t-Based Confidence Interval for the Difference between Two Population Means: Equal Variances S uppose we have randomly selected independent samples from two normally distributed populations having equal variances Then, a 100(1 ؊ A) percent confidence interval for M1 ؊ M2 is B ( x Ϫ x ) Ϯ ta͞2 B s2p n 1 ϩ R n2 where s2p ϭ (n Ϫ 1)s21 ϩ (n Ϫ 1)s22 n1 ϩ n2 Ϫ and t a͞2 is based on (n ϩ n Ϫ 2) degrees of freedom EXAMPLE 10.1 The Catalyst Comparison Case: Process Improvement A production supervisor at a major chemical company must determine which of two catalysts, catalyst XA-100 or catalyst ZB-200, maximizes the hourly yield of a chemical process In order to compare the mean hourly yields obtained by using the two catalysts, the supervisor runs the process using each catalyst for five one-hour periods The resulting yields (in pounds per hour) C bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 384 www.downloadslide.com 384 Chapter 10 Yields of a Chemical Process Obtained Using Two Catalysts Catalyst XA-100 Catalyst ZB-200 801 814 784 836 820 x1 ؍811 752 718 776 742 763 x2 ؍750.2 s21 ؍386 s22 ؍484.2 DS Catalyst Boxplot of XA-100, ZB-200 820 Yield TA B L E Comparing Two Means and Two Proportions 770 720 XA-100 ZB-200 for each catalyst, along with the means, variances, and box plots2 of the yields, are given in Table 10.1 Assuming that all other factors affecting yields of the process have been held as constant as possible during the test runs, it seems reasonable to regard the five observed yields for each catalyst as a random sample from the population of all possible hourly yields for the catalyst Furthermore, because the sample variances s21 ϭ 386 and s22 ϭ 484.2 not differ substantially (notice that s1 ϭ 19.65 and s2 ϭ 22.00 differ by even less), it might be reasonable to conclude that the population variances are approximately equal.3 It follows that the pooled estimate (n Ϫ 1)s21 ϩ (n Ϫ 1)s22 n1 ϩ n2 Ϫ (5 Ϫ 1)(386) ϩ (5 Ϫ 1)(484.2) ϭ ϭ 435.1 5ϩ5Ϫ2 s2p ϭ is a point estimate of the common variance s2 We define m1 as the mean hourly yield obtained by using catalyst XA-100, and we define m2 as the mean hourly yield obtained by using catalyst ZB-200 If the populations of all possible hourly yields for the catalysts are normally distributed, then a 95 percent confidence interval for m1 Ϫ m2 is B( x Ϫ x 2) Ϯ t 025 df ϭ 025 B s2p n R n2 ϭ B(811 Ϫ 750.2) Ϯ 2.306 025 95 Ϫt.025 ϩ B 435.1 5 ϩ 5 R 1 ϭ [60.8 Ϯ 30.4217] ϭ [30.38, 91.22] t.025 2.306 Here t.025 ϭ 2.306 is based on n1 ϩ n2 Ϫ ϭ ϩ Ϫ ϭ degrees of freedom This interval tells us that we are 95 percent confident that the mean hourly yield obtained by using catalyst XA-100 is between 30.38 and 91.22 pounds higher than the mean hourly yield obtained by using catalyst ZB-200 Suppose we wish to test a hypothesis about m1 Ϫ m2 In the following box we describe how this can be done Here we test the null hypothesis H0: m1 Ϫ m2 ϭ D0, where D0 is a number whose value varies depending on the situation Often D0 will be the number In such a case, the null hypothesis H0: m1 Ϫ m2 ϭ says there is no difference between the population means m1 and m2 In this case, each alternative hypothesis in the box implies that the population means m1 and m2 differ in a particular way All of the box plots presented in this chapter and in Chapter 12 have been obtained using MINITAB We describe how to test the equality of two variances in Chapter 11 (although, as we will explain, this test has drawbacks) bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 385 www.downloadslide.com 10.1 385 Comparing Two Population Means by Using Independent Samples A t-Test about the Difference between Two Population Means: Equal Variances Null Hypothesis Test Statistic H0 : m1 Ϫ m2 ϭ D0 tϭ ( x1 Ϫ x2) Ϫ D0 1 s2p ϩ A n1 n2 Assumptions p-Value (Reject H0 if p-Value Ͻ ␣) Critical Value Rule Ha: 1 Ϫ 2 Ͼ D0 Do not reject H0 Reject H0 Ha: 1 Ϫ 2 Ͻ D0 Reject H0 ␣ Do not reject H0 Ha: 1 Ϫ 2 ϶ D0 Reject H0 ␣ t␣ Reject H0 if t Ͼ t␣ Independent samples and Equal variances and either Normal populations or Large sample sizes Do not reject H0 Ha: 1 Ϫ 2 Ͼ D0 Reject H0 Ha: 1 Ϫ 2 ϶ D0 p-value p-value ␣ր2 ␣ր2 t␣ր2 Ϫt␣ր2 Reject H0 if ԽtԽ Ͼ t␣ր2—that is, t Ͼ t␣ր2 or t Ͻ Ϫt␣ր2 Ϫt␣ Reject H0 if t Ͻ Ϫt␣ Ha: 1 Ϫ 2 Ͻ D0 t p-value ϭ area to the right of t t p-value ϭ area to the left of t ԽtԽ ϪԽtԽ p-value ϭ twice the area to the right of ԽtԽ Here t a , t a͞2 , and the p-values are based on n ϩ n Ϫ degrees of freedom C EXAMPLE 10.2 The Catalyst Comparison Case: Process Improvement In order to compare the mean hourly yields obtained by using catalysts XA-100 and ZB-200, we will test H0: M1 ؊ M2 ؍0 versus Ha: M1 ؊ M2 at the 05 level of significance To perform the hypothesis test, we will use the sample information in Table 10.1 to calculate the value of the test statistic t in the summary box Then, because Ha: m1 Ϫ m2 implies a two tailed test, we will reject H0: M1 ؊ M2 ؍0 if the absolute value of t is greater than tA͞2 ؍t.025 ؍2.306 Here the ta͞2 point is based on n1 ϩ n2 Ϫ ϭ ϩ Ϫ ϭ degrees of freedom Using the data in Table 10.1, the value of the test statistic is df ϭ ␣/2 ϭ 025 ␣/2 ϭ 025 Ϫt.025 Ϫ2.306 t.025 2.306 000868 tϭ ( x1 Ϫ x2) Ϫ D0 (811 Ϫ 750.2) Ϫ ϭ ϭ 4.6087 1 1 s ϩ 435.1 ϩ A p n1 n2 A 5 Because Η t Η ؍4.6087 is greater than t.025 ؍2.306, we can reject H0: M1 ؊ M2 ؍0 in favor of Ha: M1 ؊ M2 We conclude (at an a of 05) that the mean hourly yields obtained by using the two catalysts differ Furthermore, the point estimate x1 Ϫ x2 ϭ 811 Ϫ 750.2 ϭ 60.8 says we estimate that the mean hourly yield obtained by using catalyst XA-100 is 60.8 pounds higher than the mean hourly yield obtained by using catalyst ZB-200 Figure 10.2(a) gives the Excel output for using the equal variance t statistic to test H0 versus Ha The output tells us that t ϭ 4.6087 and that the associated p-value is 001736 This very small p-value tells us that we have very strong evidence against H0: m1 Ϫ m2 ϭ and in favor of Ha: m1 Ϫ m2 In other words, we have very strong evidence that the mean hourly yields obtained by using the two catalysts differ (Note that in Figure 10.2(b) we give the Excel output for using an unequal variances t statistic, which is discussed on the following pages, to perform the hypothesis test.) Ϫ4.6087 000868 |t | 4.6087 p-value ϭ 2(.000868) ϭ 001736 BI bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 386 www.downloadslide.com 386 Chapter 10 FIGURE 10.2 Comparing Two Means and Two Proportions Excel Outputs for Testing the Equality of Means in the Catalyst Comparison Case (a) The Excel Output Assuming Equal Variances (b) The Excel Output Assuming Unequal Variances t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Diff df t Stat P(TϽϭt) one-tail t Critical one-tail P(TϽϭt) two-tail t Critical two-tail s22 XA-100 811 386 435.1 4.608706 0.000868 1.859548 0.001736 2.306004 ZB-200 750.2 484.2 Mean Variance Observations Hypothesized Mean Diff df t Stat P(TϽϭt) one-tail t Critical one-tail P(TϽϭt) two-tail t Critical two-tail XA-100 811 386 4.608706 0.000868 1.859548 0.001736 2.306004 ZB-200 750.2 484.2 When the sampled populations are normally distributed and the population variances s21 and differ, the following can be shown t-Based Confidence Intervals for M1 ؊ M2, and t-Tests about M1 ؊ M2: Unequal Variances When the sample sizes n1 and n2 are equal, the “equal variances” t-based confidence interval and hypothesis test given in the preceding two boxes are approximately valid even if the population variances s21 and s22 differ substantially As a rough rule of thumb, if the larger sample variance is not more than three times the smaller sample variance when the sample sizes are equal, we can use the equal variances interval and test Suppose that the larger sample variance is more than three times the smaller sample variance when the sample sizes are equal or suppose that both the sample sizes and the sample variances differ substantially Then, we can use an approximate procedure that is sometimes called an “unequal variances” procedure This procedure says that an approximate 100(1 ؊ A) percent confidence interval for M1 ؊ M2 is B( x1 Ϫ x2) Ϯ ta͞2 A s21 s2 ϩ 2R n1 n2 Furthermore, we can test H0 : m1 Ϫ m2 ϭ D0 by using the test statistic tϭ ( x Ϫ x 2) Ϫ D0 s21 s2 ϩ B n1 n and by using the previously given critical value and p-value conditions For both the interval and the test, the degrees of freedom are equal to df ϭ (s21͞n ϩ s22͞n 2) (s21͞n 1) (s2͞n ) ϩ 2 n1 Ϫ n2 Ϫ Here, if df is not a whole number, we can round df down to the next smallest whole number In general, both the “equal variances” and the “unequal variances” procedures have been shown to be approximately valid when the sampled populations are only approximately normally distributed (say, if they are mound-shaped) Furthermore, although the above summary box might seem to imply that we should use the unequal variances procedure only if we cannot use the equal variances procedure, this is not necessarily true In fact, because the unequal variances procedure can be shown to be a very accurate approximation whether or not the population variances are equal and for most sample sizes (here, both n1 and n2 should be at least 5), many statisticians believe that it is best to use the unequal variances procedure in almost every situation If each of n1 and n2 is large (at least 30), both the equal variances procedure and the unequal variances procedure are approximately valid, no matter what probability distributions describe the sampled populations bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 387 www.downloadslide.com 10.1 387 Comparing Two Population Means by Using Independent Samples To illustrate the unequal variances procedure, consider the bank customer waiting time situation, and recall that m1 Ϫ m2 is the difference between the mean customer waiting time under the current system and the mean customer waiting time under the new system Because of cost considerations, the bank manager wants to implement the new system only if it reduces the mean waiting time by more than three minutes Therefore, the manager will test the null hypothesis H0: M1 ؊ M2 ؍3 versus the alternative hypothesis Ha: M1 ؊ M2 Ͼ If H0 can be rejected in favor of Ha at the 05 level of significance, the manager will implement the new system Recall that a random sample of n1 ϭ 100 waiting times observed under the current system gives a sample mean x ϭ 8.79 and a sample variance s21 ϭ 4.8237 Also, recall that a random sample of n2 ϭ 100 waiting times observed during the trial run of the new system yields a sample mean x ϭ 5.14 and a sample variance s22 ϭ 1.7927 Because each sample is large, we can use the unequal variances test statistic t in the summary box The degrees of freedom for this statistic are df ϭ ϭ (s21͞n1 ϩ s22͞n2)2 (s21͞n1)2 (s2͞n )2 ϩ 2 n1 Ϫ n2 Ϫ [(4.8237͞100) ϩ (1.7927͞100)]2 (4.8237͞100)2 (1.7927͞100)2 ϩ 99 99 ϭ 163.657 which we will round down to 163 Therefore, because Ha: m1 Ϫ m2 Ͼ implies a right tailed test, we will reject H0: M1 ؊ M2 ؍3 if the value of the test statistic t is greater than tA ؍t.05 ؍1.65 (which is based on 163 degrees of freedom and has been found using a computer) Using the sample data, the value of the test statistic is df ϭ 163 ␣ ϭ 05 tϭ (x1 Ϫ x2) Ϫ s21 s2 ϩ A n1 n2 ϭ t.05 1.65 (8.79 Ϫ 5.14) Ϫ 65 ϭ ϭ 2.53 4.8237 1.7927 25722 ϩ A 100 100 p-value ϭ 006 t 2.53 Because t ؍2.53 is greater than t.05 ؍1.65, we reject H0: M1 ؊ M2 ؍3 in favor of Ha: M1 ؊ M2 Ͼ We conclude (at an a of 05) that m1 Ϫ m2 is greater than and, therefore, that the new system reduces the population mean customer waiting time by more than minutes Therefore, the bank manager will implement the new system Furthermore, the point estimate x1 Ϫ x2 ϭ 3.65 says that we estimate that the new system reduces mean waiting time by 3.65 minutes Figure 10.3 gives the MINITAB output of using the unequal variances procedure to test H0: m1 Ϫ m2 ϭ versus Ha: m1 Ϫ m2 Ͼ The output tells us that t ϭ 2.53 and that the associated p-value is 006 The very small p-value tells us that we have very strong evidence against H0: m1 Ϫ m2 ϭ and in favor of Ha: m1 Ϫ m2 Ͼ That is, we have very strong evidence that m1 Ϫ m2 is greater than and, therefore, that the new system reduces the mean customer waiting time by more than minutes To find a 95 percent confidence interval for m1 Ϫ m2, note that we can use a computer to find that t.025 based on 163 degrees of freedom is 1.97 It follows that the 95 percent confidence interval for m1 Ϫ m2 is BI df ϭ 163 025 025 95 Ϫt.025 t.025 1.97 s21 s22 4.8237 1.7927 B(x1 Ϫ x2) Ϯ t.025 ϩ R ϩ R ϭ B(8.79 Ϫ 5.14) Ϯ 1.97 A n1 n2 A 100 100 ϭ [3.65 Ϯ 50792] ϭ [3.14, 4.16] This interval says that we are 95 percent confident that the new system reduces the mean of all customer waiting times by between 3.14 minutes and 4.16 minutes bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 388 www.downloadslide.com 388 Chapter 10 FIGURE 10.3 Comparing Two Means and Two Proportions MINITAB Output of the Unequal Variances Procedure for the Bank Customer Waiting Time Situation N 100 100 Mean 8.79 5.14 StDev 2.20 1.34 MINITAB Output of the Unequal Variances Procedure for the Catalyst Comparison Case Two-Sample T-Test and CI: XA-100, ZB-200 Two-Sample T-Test and CI Sample Current New FIGURE 10.4 SE Mean 0.22 0.13 Difference = mu(1) - mu(2) Estimate for difference: 3.650 95% lower bound for difference: 3.224 T-Test of difference = (vs >): T-Value = 2.53 P-Value = 0.006 DF = 163 XA-100 ZB-200 N 5 Mean 811.0 750.2 StDev 19.6 22.0 SE Mean 8.8 9.8 Difference = mu (XA-100) - mu (ZB-200) Estimate for difference: 60.8000 95% CI for difference: (29.6049, 91.9951) T-Test of difference = (vs not =): T-Value = 4.61 P-Value = 0.002 DF = In general, the degrees of freedom for the unequal variances procedure will always be less than or equal to n1 ϩ n2 Ϫ 2, the degrees of freedom for the equal variances procedure For example, if we use the unequal variances procedure to analyze the catalyst comparison data in Table 10.1, we can calculate df to be 7.9 This is slightly less than n1 ϩ n2 Ϫ ϭ ϩ Ϫ ϭ 8, the degrees of freedom for the equal variances procedure Figure 10.2(b) gives the Excel output, and Figure 10.4 gives the MINITAB output, of the unequal variances analysis of the catalyst comparison data Note that the Excel unequal variances procedure rounds df ϭ 7.9 up to and obtains the same results as did the equal variances procedure (see Figure 10.2(a)) On the other hand, MINITAB rounds df ϭ 7.9 down to and finds that a 95 percent confidence interval for m1 Ϫ m2 is [29.6049, 91.9951] MINITAB also finds that the test statistic for testing H0: m1 Ϫ m2 ϭ versus Ha: m1 Ϫ m2 is t ϭ 4.61 and that the associated p-value is 002 These results not differ by much from the results given by the equal variances procedure To conclude this section, it is important to point out that if the sample sizes n1 and n2 are not large (at least 30), and if we fear that the sampled populations might be far from normally distributed, we can use a nonparametric method One nonparametric method for comparing populations when using independent samples is the Wilcoxon rank sum test This test is discussed in Chapter 18 Exercises for Section 10.1 CONCEPTS For each of the formulas described below, list all of the assumptions that must be satisfied in order to validly use the formula 10.1 The confidence interval in the formula box on page 383 10.2 The hypothesis test described in the formula box on page 385 10.3 The confidence interval and hypothesis test described in the formula box on page 386 METHODS AND APPLICATIONS Suppose we have taken independent, random samples of sizes n1 ϭ and n2 ϭ from two normally distributed populations having means m1 and m2, and suppose we obtain x ϭ 240, x ϭ 210, s1 ϭ 5, and s2 ϭ Using the equal variances procedure, Exercises 10.4, 10.5, and 10.6 10.4 Calculate a 95 percent confidence interval for m1 Ϫ m2 Can we be 95 percent confident that m1 Ϫ m2 is greater than 20? Explain why we can use the equal variances procedure here 10.5 Use critical values to test the null hypothesis H0: m1 Ϫ m2 Յ 20 versus the alternative hypothesis Ha: m1 Ϫ m2 Ͼ 20 by setting a equal to 10, 05, 01, and 001 How much evidence is there that the difference between m1 and m2 exceeds 20? 10.6 Use critical values to test the null hypothesis H0: m1 Ϫ m2 ϭ 20 versus the alternative hypothesis Ha: m1 Ϫ m2 20 by setting a equal to 10, 05, 01, and 001 How much evidence is there that the difference between m1 and m2 is not equal to 20? 10.7 Repeat Exercises 10.4 through 10.6 using the unequal variances procedure Compare your results to those obtained using the equal variances procedure bow21493_ch10_380-411.qxd 11/29/12 2:29 PM Page 389 www.downloadslide.com 10.1 Comparing Two Population Means by Using Independent Samples 10.8 An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.63 percent with a standard deviation of 31 percent, and an independent random sample of 12 municipal bond funds gives a mean annual expense of 0.89 percent with a standard deviation of 23 percent Let m1 be the mean annual expense for stock funds, and let m2 be the mean annual expense for municipal bond funds Do parts a, b, and c by using the equal variances procedure Then repeat a, b, and c using the unequal variances procedure Compare your results a Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger than the mean annual expense for municipal bond funds Test these hypotheses at the 05 level of significance What you conclude? b Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the mean annual expense for municipal bond funds by more than percent Test these hypotheses at the 05 level of significance What you conclude? c Calculate a 95 percent confidence interval for the difference between the mean annual expenses for stock funds and municipal bond funds Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than percent? Explain In the book Business Research Methods, Donald R Cooper and C William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople The authors describe the situation as follows: 10.9 The company selects 22 sales trainees who are randomly divided into two experimental groups—one receives type A and the other type B training The salespeople are then assigned and managed without regard to the training they have received At the year’s end, the manager reviews the performances of salespeople in these groups and finds the following results: A Group Average Weekly Sales Standard Deviation B Group –x ϭ $1,500 s1 ϭ 225 –x ϭ $1,300 s2 ϭ 251 a Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training b Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent Assuming that the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part a at levels of significance 10, 05, 01, and 001 How much evidence is there that type A training produces results that are superior to those of type B? c Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used Interpret this interval 10.10 A marketing research firm wishes to compare the prices charged by two supermarket chains— Miller’s and Albert’s The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores The stores for each chain are randomly selected, and all purchases are made during a single week The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows: DS ShopExp 124 $119.25 $123.71 $121.32 $121.72 $122.34 $122.42 $120.14 $123.63 $122.19 $122.44 $114.88 $115.38 $115.11 $114.40 $117.02 $113.91 $116.89 $111.87 Albert’s $111.99 $116.62 Expense Miller’s 119 114 Miller Albert Market Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed a Letting mM be the mean weekly expense for the shopping plan at Miller’s, and letting mA be the mean weekly expense for the shopping plan at Albert’s, Figure 10.5 gives the MINITAB output of the test of H0: mM Ϫ mA ϭ (that is, there is no difference between mM and mA) versus Ha: mM Ϫ mA (that is, mM and mA differ) Note that MINITAB has employed the 389 bow21493_ref_814-815.qxd 11/30/12 12:16 PM Page 815 www.downloadslide.com References Dielman, Terry Applied Regression Analysis for Business and Economics Belmont, CA: Duxbury Press, 1996 Dillon, William R., Thomas J Madden, and Neil H Firtle Essentials of Marketing Research Homewood, IL: Richard D Irwin Inc., 1993, pp 382–84, 416–17, 419–20, 432–33, 445, 462–64, 524–27 Dondero, Cort “SPC Hits the Road.” Quality Progress, January 1991, pp 43–44 Draper, N., and H Smith Applied Regression Analysis 2nd ed New York, NY: John Wiley & Sons, 1981 Farnum, Nicholas R Modern Statistical Quality Control and Improvement Belmont, CA: Duxbury Press, 1994, p 55 Fitzgerald, Neil “Relations Overcast by Cloudy Conditions.” CA Magazine, April 1993, pp 28–35 Garvin, David A Managing Quality New York, NY: Free Press/Macmillan, 1988 Gibbons, J D Nonparametric Statistical Inference 2nd ed New York, NY: McGraw-Hill, 1985 Gitlow, Howard, Shelly Gitlow, Alan Oppenheim, and Rosa Oppenheim Tools and Methods for the Improvement of Quality Homewood, IL: Richard D Irwin, 1989, pp 14–25, 533–53 Guthrie, James P., Curtis M Grimm, and Ken G Smith “Environmental Change and Management Staffing: A Reply.” Journal of Management 19, no (1993), pp 889–96 Kuhn, Susan E “A Closer Look at Mutual Funds: Which Ones Really Deliver?” Fortune, October 7, 1991, pp 29–30 Kumar, V., Roger A Kerin, and Arun Pereira “An Empirical Assessment of Merger and Acquisition Activity in Retailing.” Journal of Retailing 67, no (Fall 1991), pp 321–38 Magee, Robert P Advanced Managerial Accounting New York, NY: Harper & Row, 1986, p 223 Mahmood, Mo Adam, and Gary J Mann “Measuring the Organizational Impact of Information Technology Investment: An Exploratory Study.” Journal of Management Information Systems 10, no (Summer 1993), pp 97–122 Martocchio, Joseph J “The Financial Cost of Absence Decisions.” Journal of Management 18, no (1992), pp 133–52 Mendenhall, W., and J Reinmuth Statistics for Management Economics 4th ed Boston, MA: PWS-KENT Publishing Company, 1982 The Miami University Report Miami University, Oxford, OH, vol 8, no 26, 1989 Moore, David S The Basic Practice of Statistics 2nd ed New York: W H Freeman and Company, 2000 Moore, David S., and George P McCabe Introduction to the Practice of Statistics 2nd ed New York: W H Freeman, 1993 815 Morris, Michael H., Ramon A Avila, and Jeffrey Allen “Individualism and the Modern Corporation: Implications for Innovation and Entrepreneurship.” Journal of Management 19, no (1993), pp 595–612 Neter, J., M Kutner, C Nachtsheim, and W Wasserman Applied Linear Statistical Models 4th ed Homewood, IL: Irwin/McGraw-Hill, 1996 Neter, J., W Wasserman, and M H Kutner Applied Linear Statistical Models 2nd ed Homewood, IL: Richard D Irwin, 1985 Nunnally, Bennie H., Jr., and D Anthony Plath Cases in Finance Burr Ridge, IL: Richard D Irwin, 1995, pp 12-1–12-7 Olmsted, Dan, and Gigi Anders “Turned Off.” USA Weekend, June 2–4, 1995 Ott, Lyman An Introduction to Statistical Methods and Data Analysis 2nd ed Boston, MA: PWS-Kent, 1987 Schaeffer, R L., William Mendenhall, and Lyman Ott Elementary Survey Sampling 3rd ed Boston, MA: Duxbury Press, 1986 Scherkenbach, William The Deming Route to Quality and Productivity: Road Maps and Roadblocks Washington, DC.: CEEPress Books, 1986 Seigel, James C “Managing with Statistical Models.” SAE Technical Paper 820520 Warrendale, PA: Society for Automotive Engineers, Inc., 1982 Sichelman, Lew “Random Checks Find Loan Application Fibs.” The Journal-News (Hamilton, Ohio), Sept 26, 1992 (originally published in The Washington Post) Siegel, Andrew F Practical Business Statistics 2nd ed Homewood, IL: Richard D Irwin, 1990, p 588 Silk, Alvin J., and Ernst R Berndt “Scale and Scope Effects on Advertising Agency Costs.” Marketing Science 12, no (Winter 1993), pp 53–72 Stevenson, William J Production/Operations Management 6th ed Homewood, IL: Irwin/McGraw-Hill, 1999, p 228 Thomas, Anisya S., and Kannan Ramaswamy “Environmental Change and Management Staffing: A Comment.” Journal of Management 19, no (1993), pp 877–87 Von Neumann, J., and O Morgenstern Theory of Games and Economic Behavior 2nd ed Princeton, NJ: Princeton University Press, 1947 Walton, Mary The Deming Management Method New York, NY: Dodd, Mead & Company, 1986 Weinberger, Marc G., and Harlan E Spotts “Humor in U.S versus U.K TV Commercials: A Comparison.” Journal of Advertising 18, no (1989), pp 39–44 Wright, Thomas A., and Douglas G Bonett “Role of Employee Coping and Performance in Voluntary Employee Withdrawal: A Research Refinement and Elaboration.” Journal of Management 19, no (1993) pp 147–61 bow21493_cre_816.qxd 11/30/12 12:14 PM Page 816 www.downloadslide.com Photo Credits Chapter Page 2: © Designpics/Glow Images Page 6: © Jose Luis Pelaez Inc/Blend Images LLC Page 9: © John Foxx Images/Imagestate Page 10: © Jon Feingersh/age footstock Page 14: © Janis Christie/Getty Images Page 16: © Dave Robertson/Masterfile Chapter Page 35: © Kwame Zikomo/SuperStock Page 42: © Marnie Burkhart/age footstock Page 56: © Stockbyte/Getty Images Page 61: © Hill Street Studios/Blend Images LLC Page 70: © Digital Vision/Alamy Chapter Page 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Acura, 41, 75 Addition rule, 164, 166 Adjusted multiple coefficient of determination, 568 Aeras Global TB Vaccine Foundation, 77 Aggregate index, 669 Aggregate price index, 669–670 Akaah, Ishmael P., 322, 814 Akamai Technologies, 54 Alam, Pervaiz, 478, 479 Alaska Airlines, 185 Allegiant Travel, 54 Allen, Jeffrey, 815 Alson, Jeff, 11n8 Alta Vista, Alternative (research) hypothesis, 341–343, 372; see also Hypothesis testing greater than, 347–348 less than, 350–351 not equal to, 352–353 one-sided, 343, 347–353 two-sided, 343, 370–371 Alternatives, 763, 779 Altria Group, 270 Alzheimer’s Association, 77 America West Airlines, 185 American Cancer Society, 77 American Century Equity Income Institutional Fund, 423 American Civil Liberties Foundation, 77 American Diabetes Association, 77 American Enterprise Institute, 77 American Heart Association, 77 American Jewish Joint Distribution Committee, 77 American Kidney Foundation, 77 American Museum of Natural History, 77 American National Red Cross, 77 American Nicaraguan Foundation, 77 American Productivity and Quality Center, 684 American Public Education, 54 American Society for Quality Control (ASQC), 682, 684 American SPCA, 77 American Statistical Association, 12 AmeriCares Foundation, 77 Analysis of covariance, 436 Analysis of variance (ANOVA), 427 one-way, 429–436 randomized block design, 439–442 two-way, 445–451 Analysis of variance table, 433, 440–441, 453 Anders, Gigi, 271, 815 Andrews, R L., 561 Anheuser-Busch, 270 Aniston, Jennifer, 52 ANOVA; see Analysis of variance Anti-Defamation League of B’nai B’rith, 77 Aramark, 142 Archer Daniels, 270 Arizona Diamondbacks, 54 Art Institute of Chicago, 77 Arthritis Foundation, 77 Ashton, Robert H., 335, 814 Asia Foundation, 77 Ask.com, ASQC (American Society for Quality Control), 682, 684 Assignable causes, of process variation, 686, 707–708, 725 Associated Press, 174, 208 Association of Executive Search Consultants, 287 Association of Trial Lawyers of America, 16 Atlanta Braves, 54 Atlanta Hawks, 110 AT&T, 682, 700 AT&T Consumer Communications, 684 Atwood Oceanics, 54 Audi, 75 Autocorrelation, 534–535 negative, 532 positive, 531–532 AutoExec magazine, 40 Autoregressive model, 637 Autoregressive terms, 664–665 Avila, Ramon A., 815 Axcel, Amir, 814 B Back-to-back stem-and-leaf displays, 58–59 Backward elimination, 602, 620 Balchem, 54 Baldrige, Malcolm, 683 Baldrige National Quality Awards, 683–684, 713 Baltimore Orioles, 54 Bank of America, 286–287 Bar charts, 36–37, 73, 81; see also Pareto charts Barnett, A., 185 Base time period, 669 Bayes’ theorem, 175–178, 182 Bayesian statistics, 178, 182 Bayus, Barry L., 309, 361, 814 Beattie, Vivien, 336, 814 Bechtel, 142 Bell-shaped curve, 113–114; see also Normal curve Bell Telephone, 682 Bell Telephone Laboratories, 682 Berndt, Ernst R., 309, 815 Between-treatment variability, 430 Bieber, Justin, 52 Big Brothers Big Sisters of America, 77 Billy Graham Evangelistic Association, 77 Binomial distribution, 197–206 definition, 217 mean, variance, and standard deviation, 205 normal approximation of, 248–251 Binomial experiments, 199, 217 Binomial formula, 199–200 Binomial random variables, 199, 217 Binomial tables, 201–202, 217, 783–787 Bissell, H H., 544 Bitner, Michael, 247 Bivariate normal probability distribution, 522 Black Eyed Peas, 52 Blauw, Jan Nico, 316, 814 Block, Stanley B., 77, 194–196 Block sum of squares (SSB), 440 Blodgett, Jeffrey G., 336, 814 Bloomberg, Blue Ribbon Home Mortgage, 127 BMW, 75 BMW Group, 41 Bon Jovi, 52 Bonett, Douglas G., 815 Boo, H C., 743–744 Borden Burger, 510 Boston Celtics, 110 Boston Red Sox, 54 Boston Symphony Orchestra, 77 Boundaries, class, 43 Bowerman, Bruce L., 430, 558, 564, 683, 814 Box, G E P., 639, 660, 814 Box-and-whiskers displays (box plots), 123–124, 139 Box-Jenkins methodology, 632, 637, 660–667 Boy Scouts of America, 77 Boyd, T C., 618, 814 Boys & Girls Clubs of America, 77 Branch, Shelly, 327n Brookings Institute, 77 Brother’s Brother Foundation, 77 Brown, R G., 814 Bryant, Kobe, 52 Buick, 7, 75, 116 Burger King, 510 C C statistic, 602 Cadillac, 75 Campbell Soup, 270 Campus Crusade for Christ, 77 Cap Cod Healthcare, 77 Capability studies, 707–715 Capable processes, 687, 708, 725 Capella Education, 54 CARE USA, 77 Carey, John, 814 Cargill, 142 Carslaw, Charles A P N., 309, 814 Carter Center, 77 Categorical (qualitative) variables, 4, 16; see also Qualitative variables Cateora, Philip R., 814 Catholic Charities USA, 77 Catholic Medical Mission Board, 77 Catholic Relief Services, 77 Cause-and-effect diagrams, 721–722, 725 CBS, 350 CBS News Poll Database, 406 CDC (Centers for Disease Control and Prevention), 185, 485 CEEM Information Systems, 78, 684–685 Cell frequencies, 470, 471 Cell percentages, 470–471 Census, 7, 16 Census Bureau, U.S., 5, 17 Census II method, 646 Center line (CNL), 691, 694 Centered moving averages, 641, 642 Centers for Disease Control and Prevention (CDC), 185, 485 Central Limit Theorem, 278–280, 295 Central tendency, 101–107 definition, 101, 139 mean, 101–102, 105–107 median, 103–107 mode, 104–107 Certainty, 764, 779 Chambers, S., 547 Charlotte Bobcats, 110 Charts; see Control charts; Graphs Chebyshev’s Theorem, 116–117, 139, 193 Chevrolet, 75, 78, 194 Chi-square distribution, 413, 414, 423 Chi-square goodness of fit tests, 461 for multinomial probabilities, 461–464 for normality, 465–467 Chi-square point, 372 Chi-square statistic, 462 Chi-square table, 413, 414, 794 Chi-square test for independence, 470–475, 478 Chicago Bulls, 110 Chicago Cubs, 54 Chicago White Sox, 54 ChildFund International, 77 Children International, 77 Children’s Hospital Boston, 77 Children’s Hospital Los Angeles, 77 Children’s Hospital of Philadelphia, 77 Children’s Memorial Hospital, 77 Children’s Network International, 77 Chrysler Motors, 40, 41, 74, 75, 142, 468 Cincinnati Reds, 54 Class boundaries, 43 Class lengths, 42–43, 45, 46 Class midpoints, 45, 73 Cleary, Barbara A., 40, 41 Clemen, Robert T., 184, 774, 775, 779, 780, 814 Cleveland Air Route Traffic Control Center, 208 Cleveland Cavaliers, 110 Cleveland Indians, 54 Cluster sampling, 288–289, 295 CNL (center line), 691, 694 Coast To Coast Mortgage Lending, 127 Coates, R., 16, 722 Coca-Cola Company, 270, 444–445 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 818 www.downloadslide.com 818 Coca-Cola Enterprises, 270 Coefficient of variation, 117–118, 139 Colorado Rockies, 54 Column percentages, 63 Coma (movie), 212 Common causes, of process variation, 685–686, 708, 725 Community Mortgage Services Inc., 127 Comparisonwise error rate, 434 Complement, of event, 161, 182 Completely randomized experimental design, 428, 436, 453 Composite score, ConAgra Foods, 270 Concur Technologies, 54 Conditional probability, 167–169, 182 Confidence coefficient, 304, 334 Confidence intervals definition, 301, 334 general formula, 304–307 multiple regression model, 574–577 one-sided, 354 parameters of finite populations, 328–330 for population mean, finite population, 328–329 for population mean, known standard deviation, 301–307, 317–320 for population mean, unknown standard deviation, 310–315 for population proportion, 321–325, 328 randomized block design, 441 sample sizes, 317–320, 323–325 simple linear regression, 510–513 simultaneous, 434–435 testing hypotheses with, 354 tolerance intervals vs., 315 two-sided, 354 two-way ANOVA, 450 Confidence level, 301, 303, 306, 334 Conforming units (nondefective), 715, 725 Conlon, Edward J., 814 Constant seasonal variation, 635, 636 Constant variance assumption multiple linear regression, 566 residual analysis, 529, 531 simple linear regression model, 500–501 Constants, in control charts, 693–694, 802 Consumer Price Index (CPI), 671–672 Consumer Reports, 327, 337, 376 Continental Resources, 54 Contingency table, 162, 461, 470–473, 478 Continuity correction, 249–250 Continuous probability distribution, 225–226, 258 Continuous process improvement, 685 Continuous random variables, 187–188, 217, 225 Control charts; see also R charts; x-bar charts analyzing, 691–702 center line, 691, 694 constants, 693–694, 802 control limits, 691, 694 definition, 725 development of, 682 misleading, 12 p charts, 715–718 pattern analysis, 700–702 use of, 681, 691, 713 zones, 700–702 Control group, 437 Control limits, 691 Convenience sampling, 270 Cook’s distance measure, 609–610 Cooper, Donald R., 126, 389, 476, 478, 814 Index Corbette, M F., 287n Correlation; see also Autocorrelation meaning, 520 negative, 129–130, 519 positive, 129–130, 519 Correlation coefficient, 216 definition, 139 multiple, 567–568 population, 130, 522 sample, 129–130 simple, 519–520 Spearman’s rank, 522, 750–754, 805 Correlation matrix, 598 Counting rules, 159, 179–181 Covariance, 216 analysis of, 436 definition, 127, 139, 217 population, 130 sample, 127–129 Covariates, 436 Cowell, Simon, 52 Cox Enterprises, 142 CPI (Consumer Price Index), 671–672 CPk index, 713, 725 Cravens, David W., 579 Critical points, Durbin-Watson, 637 Critical value rule, 347–350 Critical values definition, 372 Durbin-Watson statistic, 801–802 z tests, 347–348 Cross-sectional data, 4, 16, 528, 543 Cross-tabulation tables, 61–64, 73 C&S Wholesale Grocers, 142 Cumulative frequency distributions, 49–50, 73 Cumulative normal table, 232–237, 258 Cumulative percent frequencies, 50 Cumulative percent frequency distribution, 73 Cumulative percentage point, 39 Cumulative relative frequencies, 50 Cumulative relative frequency distribution, 73 Cuprisin, Tim, 814 Cycles, 631, 640 Cyclical variation, 673 D Daimler AG, 41 Dallas Mavericks, 110 D’Ambrosio, P., 547 Dartmouth College, DASL; see Data and Story Library Data; see also Observations; Variables definition, 3, 16 measurement, 688 sources, 5–6 Data and Story Library (DASL), 136, 144, 756 Data mining, 603 Data sets, 3–4 Dawson, Scott, 814 Decision criterion, 764–765, 779 Decision theory, 182, 763, 779 Bayes’ theorem, 175–178 decision making under certainty, 764 decision making under risk, 765 decision making under uncertainty, 764–765 payoffs, 763–764 posterior probabilities, 769–774 utility theory, 777 Decision trees, 197, 765–766, 779 Deckers Outdoor, 54 Defect concentration diagrams, 722, 725 Defects, p charts, 715–718; see also Quality Degrees of freedom (df), 310, 334 Deleted residuals, 609, 610 Deloitte & Touche Consulting, 42, 78 Deming, W Edwards, 682–684, 687, 814 Deming’s 14 points, 683, 684, 724 Denman, D W., 76 Denver Nuggets, 110 Dependent events, 171, 182 Dependent variables definition, 543 in experimental studies, 427 transformation, 535–538 Depp, Johnny, 52 Descriptive statistics, 8, 35; see also Central tendency; Variance definition, 16 grouped data, 133–135 misleading, 12 variation measures, 110–118 Deseasonalized time series, 643, 645, 673 Designed statistical experiments, 685 Detroit Pistons, 110 Detroit Tigers, 54 df (degrees of freedom), 310, 334 Dicaprio, Leonardo, 52 Dichotomous questions, 289–290 Dielman, Terry, 612, 815 Digital Equipment Corporation, 713 Dillon, William R., 69, 167, 322, 365, 396, 402, 405, 477, 748, 815 Discrete random variables, 187 definition, 218 mean (expected value), 190–192 probability distributions, 188–193 standard deviation, 192–193 variance, 192–193 Distance values, 511, 543, 577, 608 Distributions; see Frequency distributions Dobyns, Lloyd, 683 Dodge, 40, 41, 75, 78 Dodge, Harold F., 682 Dolby Laboratories, 54 Domino’s Pizza, 35–38 Dondero, Cort, 815 Dot plots, 54–55, 73 Double exponential smoothing, 652–654 Dow Jones & Company, Draper, N., 815 Dummy variables, 580–587, 612, 615 Dun & Bradstreet, DuPont, 684 Durbin, J., 801, 802 Durbin-Watson statistic autocorrelation and, 534, 637 critical points, 637 critical values, 801–802 Durbin-Watson test, 533–535 During, Willem E., 316, 814 E Economic indexes, 671–672 Educational Testing Service, Elber, Lynn, 174, 286 Elements, 3–4 Elliott, Robert K., 335, 814 Emenyonu, Emmanuel N., 476 Emory, C William, 126, 389, 476, 478, 814 Empirical Rule areas under normal curve and, 231, 236–237 definition, 139 for normally distributed population, 113–114 skewness and, 116–117 Energy Future Holdings, 142 ENGS (expected net gain of sampling), 774, 779 Enterprise Holdings, 142 Environmental Protection Agency (EPA), 4, 11, 116, 304 EPNS (expected payoff of no sampling), 773–774 EPS (expected payoff of sampling), 773 Ernst & Young, 142 Ernst & Young Consulting, 42 Error mean square (MSE), 432 Error sum of squares (SSE), 432, 440, 447–448 Error term, 489, 490, 534, 543 Errors of non-observation, 291–292, 295 of observation, 292–293, 295 sampling, 291 in surveys, 291–293 Estimated regression line, 491 “Ethical Guidelines for Statistical Practice,” 12 Events, 155, 157 complement, 161 definition, 155, 182 dependent, 171 independent, 170–173 intersection of, 163 mutually exclusive, 164–165 probability, 155–159 union of, 163 EVPI (expected value of perfect information), 767, 779 EVSI (expected value of sample information), 774, 779 Excel applications, 17 analysis of variance, 433, 434, 440, 442, 448, 455–456 bar charts, 36–37, 81 binomial probabilities, 201, 220 chi-square tests, 480–481 confidence intervals, 314, 337 contingency tables, 471 crosstabulation tables, 86–87 Dermal distribution, 262–263 experimental design, 455–456 frequency histograms, 47, 82–85 frequency polygons, 85 getting started, 18–23 hypergeometric probabilities, 220 hypothesis testing, 364, 377 least squares line, 145 least squares point estimates, 558 multiple linear regression, 621–622 multiplicative decomposition, 646 normal distribution, 262–263 numerical descriptive statistics, 144–147 ogives, 86 p-values, 364 Pareto charts, 38–39 pie charts, 37, 38, 82 Poisson probabilities, 221 random number generation, 297 randomized block ANOVA, 440, 442, 455 regression analysis, 583–584 runs plot, 21–22 sample correlation coefficient, 147 sample covariance, 146 scatter plots, 87 simple linear regression analysis, 505, 548–549 tabular and graphical methods, 80–87 tests for variances, 424 time series analysis, 675–676 two-sample hypothesis testing, 407 two-way ANOVA, 448, 449, 456 Expected monetary value criterion, 765, 779 Expected net gain of sampling (ENGS), 774, 779 Expected payoff of no sampling (EPNS), 773–774 Expected payoff of sampling (EPS), 773 Expected value of perfect information (EVPI), 767, 779 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 819 www.downloadslide.com 819 Index Expected value of random variable, 190–192, 218 Expected value of sample information (EVSI), 774, 779 Experimental outcomes, 153–154, 179–180 Experimental region, 494–496, 543 Experimental studies, 6, 16 Experimental units, 427–428, 453 Experiments basic design concepts, 427–429 binomial, 199 definition, 153, 182 paired differences, 391–395, 744 randomized, 427–428, 436 randomized block design, 439–442 sample spaces, 155 two-factor factorial, 446–450 variables, Experimentwise error rate, 435 Explained variation, 517–518, 543, 600 Exponential probability distribution, 252–253, 258–259 Exponential smoothing, 632, 673 defined, 632 double, 652–660 Holt-Winters’ double, 652–654 multiplicative Winters’ method, 654–659 simple, 647–652 Extreme outliers, 148 F F distribution, 404, 416–418 F point, 416–417 F table, 416–417, 795–798 F-test, 421 overall, 569–570 simple linear regression model, 522–524 FAA (Federal Aviation Administration), 208 Factors, 6, 16, 427, 453 FactSet Research Systems, 54 Farnum, Nicholas R., 140, 210, 815 Federal Aviation Administration (FAA), 208 Federal Trade Commission (FTC), 290, 364, 366 Federer, Roger, 52 Ferguson, J T., 561 F5 Networks, 54 Fidelity Investments, 142 Fidelity Small Cap Discovery Fund, 423 Finite population correction, 328 Finite population multiplier, 281 Finite populations, 10, 16, 328–330 First Data, 142 First-order autocorrelation, 534 First quartile, 121, 139 Firtle, Neil H., 69, 167, 322, 365, 396, 402, 405, 477, 815 Fishbone charts; see Cause-and-effect diagrams Fitzgerald, Neil, 327, 815 Five-number summary, 122 Florida Marlins, 54 Forbes magazine, 51–54, 77, 142 Forbes.com, 53, 54, 118 Ford, Henry, 682 Ford, John K., 296 Ford Motor Company, 40, 41, 75, 78, 468, 682, 683, 700, 725 Forecast errors, 667–668 Forrest Gump (movie), 259 Fortune magazine, 136, 287, 376, 389 Fractional power transformation, 635, 636 Frames, 288, 289 Freeman, L., 16, 722 Frequencies; see also Relative frequencies cumulative, 49–50 definition, 35 finding, 44 Frequency bar charts, 36–37, 81 Frequency distributions, 35–36, 44, 73 constructing, 45 cumulative, 49–50 mound-shaped, 47, 116–117 shapes, 47–48, 105 skewness, 47, 105–106, 116–117 Frequency histograms; see Histograms Frequency polygons, 48–49, 73 Frommer, F J., 208n2 FTC; see Federal Trade Commission G Gallup, George, 270 Gallup News Service, 66 Gallup Organization, 40, 79, 286, 376, 403, 406 Garvin, David A., 815 Gaudard, M., 16, 722 General Electric, 713 General logistic regression model, 612–614 General Mills, 270 General Motors Corporation, 10, 40, 41, 78, 153, 468, 683, 684 General multiplication rule, 169 Geometric mean, 137, 139 GeoResources, 54 George Street Research, 327 Georgetown University, 290 Giant Eagle, 142 Gibbons, J D., 749, 815 Giges, Nancy, 261 Gitlow, Howard, 683, 701, 705–707, 719, 720, 815 Gitlow, Shelly, 683, 701, 705–707, 719, 720, 815 Global Financial Data, 125 GMC, 75 Golden State Warriors, 110 GoodCarBadCar.net, 40, 41 Goodness-of-fit tests for multinomial probabilities, 461–464, 478 for normality, 465–467, 478 Google, Graduate Management Admission Council, Granbois, Donald H., 336, 814 Graphs; see also Control charts bar charts, 36–37 box-and-whiskers displays, 123–124 decision trees, 765–766 dot plots, 54–55 frequency polygons, 48–49 histograms, 42–47 misleading, 12, 70–71 ogives, 50 Pareto charts, 38–39 pie charts, 37, 38 process performance, 690–691 scatter plots, 67–68, 487 stem-and-leaf displays, 56–59 Gray, Sidney J., 476 Greater Cincinnati International Airport, 316 Greater than alternative hypothesis, 347–348, 373 Grouped data, 133–135, 139 Growth curve model, 541 Grumn, Curtis M., 815 Gunn, E P., 287n Gunter, B., 707 Gupta, S., 468 Guthrie, James P., 815 H Hald, A., 805 Hamilton Journal News, 375 Hardee’s, 510 Harrah’s Entertainment, 142 Hartley, H O., 311 HCA, 142 HE Butt Grocery, 142 Hildebrand, D K., 787, 789 Hinckley, John, 184–185 Hirt, Geoffrey A., 77, 194–196 Histograms, 42, 73 constructing, 42–47 percent frequency, 45 relative frequency, 45 Hittite Microwave, 54 HJ Heinz, 270 HMS Holdings In, 54 Hoexter, R., 723 Holt-Winters’ double exponential smoothing, 652–654 Homogeneity, test for, 464, 478 Honda, 40, 41, 75 Horizontal bar charts, 37 Houston Astros, 54 Houston Rockets, 110 Hypergeometric distribution, 206, 213–214, 218 Hypergeometric probabilities, 220–221, 223 Hypergeometric random variables, 213, 218 Hypothesis testing, 341 about population mean, 347–354 about population proportion, 361–364 alternative hypothesis, 341–343 confidence intervals, 354 legal system and, 344 null hypothesis, 341–343 one-sided alternative hypothesis, 343, 347–353 t tests, 357 two-sided alternative hypothesis, 370–371 Type I and Type II errors, 344–345, 347, 364–371 weight of evidence, 350 z tests, 347–354, 361–364 Hyundai, 41, 75 I IBM, 684, 713 Increasing seasonal variation, 635 Independence assumption chi-square test, 470–475 multiple linear regression, 566 remedies for violation of, 534–538 residual analysis, 531–533 simple linear regression model, 500–501 Independent events, 170–173, 182 Independent samples, 381–388 comparing population proportions, 398–401 comparing population variances, 418–421 Wilcoxon rank sum test, 738–742 Independent samples experiment, 404 Independent variables definition, 543 in experimental studies, 427 interaction, 585–586 multicollinearity, 597–600 significance, 571–574 Index numbers, 668–673 Indiana Pacers, 110 Indicator variables; see Dummy variables Industrial Services of America, 54 Infinite populations, 10, 16 Infiniti, 41, 75 Influential observations, 607, 609–610 Information Resources, Inc., Inner fences, 139 InnerWorkings, 54 Interaction definition, 453, 615 models, 585–586 Interaction sum of squares, 447 Interaction variables, 594–596 Interactive Intelligence, 54 InterDigital, 54 Interquartile range (IQR), 122, 139 Intersection, of events, 163 Interval variables, 14, 16 Investment Digest, 41, 140 IQR (interquartile range), 122, 139 iRobot, 54 Irregular components, 673 Irregular fluctuations, 631, 640 Ishikawa, Kaoru, 721 Ishikawa diagrams; see Cause-andeffect diagrams ISO 9000, 684–685, 725 Ito, Harumi, 405 J J D Power, 75 Jaguar, 75 James, LeBron, 52 Japan, quality control in, 682, 683, 685 Jeep, 40, 41, 74, 75 Jenkins, G M., 639, 660, 814 Jim Morrison’s MBI, 127 John, Elton, 52 Joint probability distribution, 215–217 Joint probability table, 217 Jolie, Angelina, 52 Jones, Michael John, 336, 814 Journal News, 174, 208, 286 Journal of Marketing Research, 468 Judgment sampling, 270 Julien, M., 723 Juran Institute, 722, 723 JUSE (Union of Japanese Scientists and Engineers), 683 K Kaiser Family Foundation, 286 Kansas City Royals, 54 Kaplan, Steven E., 309, 814 Kellogg, 270 Kerin, Roger A., 815 Kerrich, John, 155n, 155n1 Kerwin, Roger A., 374, 404 Kia, 41, 75 Kiewit Corporation, 142 KMG Chemicals, 54 Koch Industries, 142 Koehler, Anne B., 558, 664 Krehbiel, T C., 618, 814 Krogers, 343n2 Krohn, Gregory, 397 Kruskal-Wallis H test, 436, 748–749, 754 Kuhn, Susan E., 815 Kumar, V., 374, 404, 815 Kutner, M., 451, 587, 815 L Lady Gaga, 52, 196 Land Rover, 75 Landers, Ann, 270, 292 Landon, Alf, 270 Large sample sign test, 736 Laspeyres index, 670–671 LCL (lower control limit), 691, 694 Least squares line, 130–131, 139, 492 Least squares plane, 559 Least squares point estimates definition, 543 means, 559–560 multiple regression model, 557–559 simple linear regression model, 491–496 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 820 www.downloadslide.com 820 Least squares prediction equation, 493–494, 559 Leaves, 56, 58; see also Stem-andleaf displays Ledolter, J., 814 Lee, Darin, 405 Left-hand tail area, 235–236, 242–243 Less than alternative hypothesis, 350–351, 373 Level of significance, 347 Leverage values, 608–609 Levy, Haim, 546 Lexus, 41, 75 Liberty Mortgage, 127 Liebeck, Stella, 16 Limbaugh, Rush, 52 Lincoln, 75 Line charts; see Runs plots Line of means, 489 Linear regression models; see Multiple regression model; Simple linear regression model Linear relationships, 67, 127 Linear trend regression model, 633–634 Literary Digest poll (1936), 270, 292 Little Caesars Pizza, 35–38 Logarithmic transformation, 536, 541–542 Logistic curve, 612 Logistic regression, 611–614 Logit, 614, 615 Long-run relative frequencies, 154 LoopNet, 54 Los Angeles Angels, 54 Los Angeles Clippers, 110 Los Angeles Dodgers, 54 Los Angeles Lakers, 110 Lots, 682 Love’s Travel Stops & Country Stores, 142 Lower control limit (LCL), 691, 694 Lower limit, 123–124 Lumber Liquidators, 54 M Ma, Lan, MAD (mean absolute deviation), 667, 668 Madden, Thomas J., 69, 167, 322, 365, 396, 402, 405, 477, 815 Magee, Robert P., 247, 815 Mahmood, Mo Adam, 815 Mail surveys, 291 Major League Baseball (MLB), 40, 53, 54 Major League Soccer (MLS), 40 Makridakis, S., 540, 646 Malcolm Baldrige National Quality Awards, 683–684, 713 Mall surveys, 291 Mann, Gary J., 815 Mann-Whitney test; see Wilcoxon rank sum test MAPE (mean absolute percentage error), 667, 668 Margin of error, 301, 324–325, 334 Maris, Roger, 60 Mars (company), 142 Martocchio, Joseph J., 283, 815 Mason, J M., 544 MasterCard, 7, 166, 167, 173 Matrix algebra, 558 Maximax criterion, 764, 779 Maximin criterion, 764, 779 Maximum likelihood estimation, 612 Mazda, 41, 75 Mazis, M B., 76 McCabe, George P., 464, 474, 815 McCabe, William J., 719, 720 McCartney, Paul, 52 McDonald’s, 16, 510 Index McGee, V E., 540, 646 McGraw, Phil, 52 Mean; see also Population mean binomial random variable, 205 compared to median and mode, 104–107 derivation of, 293–294 discrete random variable, 190–192 geometric, 137 least squares point estimates, 559–560 normal distribution, 230 Poisson random variable, 211 population, 101–103 sample, 102 weighted, 132–133 Mean absolute deviation (MAD), 667, 668 Mean absolute percentage error (MAPE), 667, 668 Mean level, 488–489 Mean square error, 501–502, 566–567 Mean squared deviation (MSD), 667, 668 Mean squares, 431, 432 Measure of variation, 139 Measurement, 7, 16 data, 4, 688 scales, 14 Median, 103–107, 139; see also Population median Medifast, 54 MegaStat applications, 17 analysis of variance, 456–457 bar charts, 88 binomial probabilities, 222 box-and-whiskers display, 148 chi-square tests, 482–483 confidence intervals, 338 control charts, 729 crosstabulation tables, 90–91 dot plots, 90 experimental design, 456–457 frequency polygons, 89 getting started, 23–27 histograms, 88–89 hypergeometric probabilities, 222 hypothesis testing, 378 least squares line, 148 multiple linear regression, 623–625 multiplicative decomposition, 646 nonparametric methods, 756–758 normal distribution, 263–264 numerical descriptive statistics, 147–149 ogives, 89 Poisson probabilities, 222 random number generation, 298 runs plot, 26–27 sample correlation coefficient, 149 scatter plots, 91 simple linear regression analysis, 550–551 stem-and-leaf display, 90 tabular and graphical methods, 88–91 tests for variances, 424 time series analysis, 676–677 two-sample hypothesis testing, 408–409 Meier, Heidi Hylton, 478, 479 Meijer, 142 Memphis Grizzlies, 110 Mendenhall, W., 288, 289, 614, 815 Mercedes-Benz, 75 Mercury, 75 Merrington, M., 417, 795–797 Miami Heat, 110 Miami University of Ohio, 291, 423 Microsoft, 17 Mild outliers, 148 Milliken and Company, 684 Milwaukee Brewers, 54 Milwaukee Bucks, 110 mindWireless, MINI, 75 Minimum-variance unbiased point estimate, 280–281, 295 MINITAB applications, 17 analysis of variance, 433, 434, 458–459 bar charts, 37, 92–93 binomial probabilities, 204, 223 box-and-whiskers display, 124, 150 chi-square tests, 483–485 confidence intervals, 314–315, 339 contingency tables, 470–471 control charts, 730–731 crosstabulation tables, 98 distance values, 577 dot plots, 97 double exponential smoothing, 653–655 experimental design, 458–459 exponential smoothing, 651 frequency histograms, 46, 95–96 frequency polygons, 96 getting started, 27–33 hypergeometric probabilities, 223 hypothesis testing, 358, 379 least squares line, 150 least squares point estimates, 558 logistic regression, 611–613 multiple linear regression, 626–629 multiplicative decomposition, 646 nonparametric methods, 759–761 normal distribution, 264–265 normal plot, 530 numerical descriptive statistics, 149–151 ogives, 97 pie charts, 94 Poisson distribution, 210 random number generation, 298 randomized block ANOVA, 440, 442, 459 regression analysis, 583–584 runs plots, 29–30 sample correlation coefficient, 151 sample covariance, 151 sampling distribution of sample mean, 278–280, 299 scatter plots, 99 simple linear regression analysis, 505, 552–553 stem-and-leaf display, 57–58, 98 stepwise regression, 603–604 tabular and graphical methods, 92–99 tests for variances, 424 time series analysis, 678–679 two-sample hypothesis testing, 410–411, 425 two-way ANOVA, 448, 449, 459 Winters’ method, 656–659 MINITAB Inc., 17 Minnesota Timberwolves, 110 Minnesota Twins, 54 Misleading information, 12 Mitsubishi, 75 MLB; see Major League Baseball MLS (Major League Soccer), 40 Mode, 104–107, 139 Model building comparing models, 600–602 iterative selection procedure, 602–605 multicollinearity, 597–600 Moms, Michael H., 815 Moore, David S., 464, 474, 743, 815 Morgenstern, O., 777, 815 Morningstar.com, 423 Mortgage First, 127 Motorola, Inc., 684, 713 Mound-shaped distributions, 47, 116–117, 139 Moving average terms, 665–667 Moving averages, 641–642, 673 MSD (mean squared deviation), 667, 668 MSE (error mean square), 432 MST (treatment mean square), 432 Multicollinearity, 597–600, 615 Multinomial experiments, 461–462, 478 Multiple choice questions, 289–290 Multiple coefficient of determination, 567–568 Multiple correlation coefficient, 567–568 Multiple regression model, 534, 555–561, 615 assumptions, 565–566 confidence intervals, 574–577 least squares point estimates, 557–559 mean square error, 566–567 multiple coefficient of determination, 567–568 multiple correlation coefficient, 567–568 overall F-test, 569–570 point estimation, 559–560 point prediction, 560 prediction interval, 575–577 regression parameters, 556–557, 560 residual analysis, 604–607 significance of independent variable, 571–574 standard error, 566–567 Multiplication rule general, 169 for independent events, 172 Multiplicative decomposition, 636, 640–647 Multiplicative Winters’ method, 654–659 Multistage cluster sampling, 288–289 Murphree, Emily S., 814 Mutually exclusive events, 164–165, 182 N Nachtsheim, C., 451, 587, 815 NADA (National Automobile Dealers Association), 40 NASA, 207 Nascar, 118, 119 National Automobile Dealers Association (NADA), 40 National Basketball Association (NBA), 40, 109, 110 National Football League (NFL), 40 National Golf Association, 422, 438 National Hockey League (NHL), 40 National Inquirer, 293 National Presto Industries, 54 Natural tolerance limits, 708, 725 NBA; see National Basketball Association NBA Players Association, 109 NBC, 350, 683 Neff, Robert, 814 Negative autocorrelation, 532, 543, 637 Negative correlation, 129–130 Nelson, John R., 76 Neter, J., 451, 587, 815 Netscape, New Jersey Nets, 110 New Orleans Hornets, 110 New York Knicks, 110 New York Mets, 54 New York Yankees, 54, 60 NFL (National Football League), 40 NHL (National Hockey League), 40 Nissan, 40, 41, 75 No trend regression model, 632–633 Nominative variables, 14–16 Nonconforming units (defective), 715, 725 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 821 www.downloadslide.com 821 Index Nonparametric methods, 75, 315, 359, 734 advantages, 746 definition, 754 Kruskal-Wallis H test, 436, 748–749 sign test, 734–737 Spearman’s rank correlation coefficient, 522, 750–753 Wilcoxon rank sum test, 388, 738–742 Wilcoxon signed ranks test, 395, 744–746 Nonresponse, 292, 295 Normal curve, 113–114, 139 areas under, 231–237 cumulative areas under, 232–237 left-hand tail area, 235–236, 242–243 points on horizontal axis, 240–244 properties, 230–231 right-hand tail area, 234, 235, 240–242 standard, areas under, 790–791, 805 Normal distribution, 113–114, 230 approximation of binomial distribution, 248–251 goodness of fit test, 465–467 Normal probability distribution, 230, 238, 259; see also Probability distributions Normal probability plot, 259, 530 constructing, 255–256, 258 definition, 543 interpreting, 256–258 Normal table, 231, 805 cumulative, 232–237, 790–791 tolerance intervals, 244 Normality assumption chi-square goodness of fit test, 465–467 multiple linear regression, 566 residual analysis, 530 simple linear regression model, 500–501 Not equal to alternative hypothesis, 352–353, 373 Null hypothesis, 341–343, 373; see also Hypothesis testing Nunnally, Bennie H., Jr., 402, 815 NutriSystem, 54 O Oakland Athletics, 54 Observational studies, 6, 16 Observations, 7, 427 errors, 292–293, 295 influential, 607, 609–610 O’Connell, Richard T., 430, 558, 664, 683, 814 O’Connor, Catherine, 397 Odds, 613 Odds ratio, 613, 614 Ogives, 50, 73 Ohio State University, 69 Oklahoma City Thunder, 110 Olds, E G., 805 Olmsted, Dan, 271, 815 One-sided alternative hypothesis, 343, 347–353, 373 One-way ANOVA, 429–436 assumptions, 429 between-treatment variability, 431 definition, 453 estimation, 433 pairwise comparisons, 433–435 testing for significant differences between treatment means, 430–433 within-treatment variability, 430–432 Open-ended questions, 289–290 The Open University, 545 Oppenheim, Alan, 683, 701, 705–707, 719, 720, 815 Oppenheim, Rosa, 683, 701, 705–707, 719, 720, 815 Ordinal variables, 14, 16, 663, 752–753 Orlando Magic, 110 Orris, J B., 23, 793 Ott, L., 288, 289, 787, 789, 815 Outer fences, 148 Outliers dealing with, 609–610 definition, 73, 124, 139 detecting, 55, 59, 124, 607 mild and extreme, 124 Overall F-test, 569–570 Ozanne, M R., 287n P p charts, 715–718, 725 p-value (probability value), 348–351, 353, 364, 373 Paasche index, 671 Paired differences experiment, 391–395, 404, 744 Pairwise comparisons, 433–456 Papa John’s Pizza, 35–38 Parabola, 592 Parameters binomial distribution, 205 Poisson distribution, 223 population, 101, 139 regression, 490, 556–557, 560 Pareto, Vilfredo, 38 Pareto charts, 38–39, 73 Pareto principle, 38 Pattern analysis, 700–702, 725 Patterson, Roger C., 215 Payoff table, 763–764, 779 Pearson, E S., 311 Pearson, Michael A., 478, 479 Pepsi Bottling Group, 270 PepsiCo, 270 Percent bar charts, 37 Percent frequencies, 36, 45, 50 Percent frequency distributions, 36, 44, 73 Percent frequency histograms, 45 Percentage points, 324–325 Percentiles, 120–122, 139; see also Quartiles Pereira, Arun, 374, 404, 815 Perfect information, 767, 779 Perry, E S., 76 Perry, Katy, 52 Perry, Tyler, 52 Petersen, Donald, 683 Pfaffenberger, James H., 215 Philadelphia Phillies, 54 Philadelphia 76ers, 110 Philip Morris, 76 Phoenix Suns, 110 Phone surveys, 290–291 Pie charts, 37, 38, 73 Pilkington, G B., II, 544 Pilot Flying J, 142 Pittsburgh Pirates, 54 Pizza Hut, 35–38 Plane of means, 556, 559 Plath, D Anthony, 402, 815 Point estimates, 101, 139; see also Least squares point estimates minimum-variance unbiased, 280–281 randomized block design, 441 two-way ANOVA, 450 unbiased, 273, 280–281 Poisson distribution, 207–211 definition, 218 mean, variance, and standard deviation, 211 Poisson probability table, 208–209, 787–789 Poisson random variable, 207–208, 211, 218 Polling Report, 406 Pooled estimates, 383 Population correlation coefficient, 130, 521–522 Population covariance, 130 Population mean, 101, 139 comparing using independent samples, variances known, 381–388 comparing using independent samples, variances unknown, 383–388 confidence intervals, finite population, 328–329 confidence intervals, known standard deviation, 301–307, 317–320 confidence intervals, unknown standard deviation, 310–315 grouped data, 135 point estimate, 102–103 t tests, 357–359 z tests, 347–354 Population median large sample sign test, 736 sign test, 734–737 Population parameters, 101, 139 Population proportion comparing using large, independent samples, 398–401 confidence intervals, 321–325 confidence intervals, finite population, 328 z tests, 361–364 Population rank correlation coefficient, 751 Population standard deviation, 111–112, 139 Population total, 328, 334 Population variance, 111–112, 139 comparing with independent samples, 418–421 grouped data, 135 statistical inference, 414–415 Populations, 7–8 comparing, 381 definition, 7, 16 finite, 10, 328–330 infinite, 10 Porsche, 41, 75 Portland Trail Blazers, 110 Positive autocorrelation, 531–532, 543, 637 Positive correlation, 129–130 Posterior decision analysis, 769–774, 779 Posterior probability, 175–178, 182, 769–774, 779 Power, of statistical test, 369, 373 PPI (Producer Price Index), 671, 672 PQ Systems, Inc., 40 Prediction interval, 510–513, 575–577 Preliminary samples, 319 Preposterior analysis, 773, 779 Price indexes, 669–672 PricewaterhouseCoopers, 142 Prior decision analysis, 769, 779 Prior probability, 175, 182, 765 Probability, 153–155 classical, 154 conditional, 167–169 of event, 155–159, 182 subjective, 155 Probability curves, 225–226 Probability density function, 225 Probability distributions; see also Binomial distribution; Normal distribution continuous, 225–226 of discrete random variable, 188–193, 218 uniform, 227–229 Probability revision table, 770–771 Probability rules, 161 addition rule, 164, 166 multiplication rule, 169, 172 rule of complements, 161 Probability sampling, 270 Processes; see also Statistical process control capability, 687, 708 capability studies, 707–715 causes of variation, 685–687, 707–708 definition, 10, 16 performance graphs, 690–691 sampling, 687–692 variation, 685–687 Procter & Gamble Company, 683 Producer Price Index (PPI), 671, 672 Professional Mortgage Corporation, 127 Professional Valley Mortgage, 127 Proportion; see Population proportion; Sample proportion pth percentile, 120–121 Publix Super Markets, 142 Q Quadratic regression model, 592–596 Qualitative data, graphical summaries; see Bar charts; Pie charts Qualitative variables, definition, 16 dummy variables, 580–587 measurement scales, 14–15 Quality Baldrige National Quality Awards, 683–684, 713 definitions, 681–682 ISO 9000 standard, 684–685 Pareto principle, 38 sigma level capability, 711–713 total quality management, 683 Quality control; see also Statistical process control history, 682–683 inspection approach, 685 in Japan, 682, 683, 685 Quality of conformance, 681, 725 Quality of design, 681, 725 Quality of performance, 681, 725 Quality Progress, 286 Quality Systems, 54 Quality Systems Update, 78 Quantitative data, graphical summaries; see Frequency distributions; Histograms Quantitative variables, 4, 14, 16 Quantity index, 669 Quartic root transformation, 536 Quartiles, 121–122 Queueing theory, 253, 259 Queues, 253 Quiznos, 487 R R charts, 691–699 analyzing, 691–702 center line, 694 constants, 802 control limits, 694 definition, 725 pattern analysis, 700–702 Rackspace Hosting, 54 Ramaswamy, Kannan, 815 Random number table, 8, 268–269, 295 Random samples, 8–10, 267–270, 295 Random selections, 267 Random variables, 187; see also Discrete random variables binomial, 199 continuous, 187–188, 225 definition, 218 hypergeometric, 213 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 822 www.downloadslide.com 822 Randomized block design, 436, 439–442, 453 confidence intervals, 441 point estimates, 441 Ranges, 110–111 definition, 139 interquartile, 122 Ranking, 14, 733 Ranks, 752–753 Rare event approach, 203 Rasmussen Reports, 406 Ratio variables, 14, 16 Rational subgroups, 688–689, 700, 725 The Real Estate Appraiser and Analyst, 499 Rebalancing, 78 Recording errors, 292 Regression analysis, 487; see also Multiple regression model; Simple linear regression model analysis of covariance, 436 comparing models, 600–602 quadratic model, 592–596 Regression assumptions, 500–501 Regression model, 487, 488 Regression parameters, 490, 556–557, 560 Regression residuals, 527; see also Residuals Reinmuth, J., 815 Rejection points, 352; see also Critical value rule Relative frequencies cumulative, 50 definition, 36, 44, 45 long-run, 154 Relative frequency distributions, 36, 44, 73 Relative frequency histograms, 45 Replication, 427, 453 Research hypothesis; see Alternative (research) hypothesis Resident Lending Group Inc., 127 Residual analysis assumption of correct functional form, 530, 531 constant variance assumption, 529, 531 independence assumption, 531–533 multiple regression model, 604–607 normality assumption, 530 simple linear regression model, 527–534 Residual plots, 527, 543 Residuals definition, 543 deleted, 609, 610 regression, 527 studentized, 609, 610 studentized deleted, 609, 610 sum of squared, 492, 542–543, 557 Response bias, 292–293, 295 Response rates, 290–291, 295 Response variables, 6, 16, 427, 453 Reyes Holdings, 142 Reynolds American, 270 Right-hand tail area, 234, 235, 240–242 Ringold, D J., 76 Riordan, Edward A., 322, 814 Risk, 764, 765, 779 Risk averter’s curve, 777 Risk neutral’s curve, 777 Risk seeker’s curve, 777 Ritz Carlton Hotels, 684 Romig, Harold G., 682 Roosevelt, Franklin D., 270 Row percentages, 63 Rudd, Ralph, 316 Rule of complements, 161 Runs, 701, 725 Index Runs plots, 4, 16, 68 Ruth, Babe, 60 S Sacramento Kings, 110 Sample autocorrelation function (SAC), 662–667 Sample block means, 439 Sample correlation coefficient, 129–130 Sample covariance, 127–129 Sample frames, 288, 289, 291–292, 295 Sample mean, 102 definition, 139 derivation of, 293–294 grouped data, 133–134 Sample partial autocorrelation function (SPAC), 663–667 Sample proportion, 284–285 Sample sizes, 102 for confidence interval for population proportion, 323–325 for confidence interval for sample mean, 317–320 definition, 139 reducing error probabilities, 370 in stratified random sampling, 333–334 Sample space outcomes, 155–159, 182 Sample spaces, 153, 155, 182 Sample standard deviation, 112–113, 139 Sample statistic, 101–102 definition, 139 sampling distribution, 280–281 Sample treatment means, 439 Sample variance, 112–113, 134–135, 139 Samples cluster, 288–289 definition, 7, 16 preliminary, 319 random, 8–10, 267–270 sizes, 290 stratified random, 287–288 systematic, 289 voluntary response, 270, 292 Sampling acceptance, 682 convenience, 270 improper, 12 judgment, 270 probability, 270 processes, 687–691 with replacement, 267, 295 without replacement, 213–214, 267–268, 295 undercoverage, 292 Sampling designs, 287–289 Sampling distribution comparing population means, 382, 404 Sampling distribution comparing population proportions, 398–401, 404 Sampling distribution comparing population variances, 404, 418 Sampling distribution of sample mean, 271–278, 295 Central Limit Theorem, 278–280 unbiasedness and minimumvariance estimates, 280–281 Sampling distribution of sample proportion, 284–285, 295 Sampling distribution of sample statistic, 280–281, 295 Sampling error, 291, 295 San Antonio Spurs, 110 San Diego Padres, 54 San Francisco Giants, 54 Sapient, 54 Sara Lee, 270 SC Johnson & Son, 142 Scanner panels, 468 Scatter plots, 67–68, 73–74, 487 Schaeffer, R L., 288, 289, 815 Schargel, Franklin P., 724 Scheffe, Henry, 800 Scherkenbach, William, 683, 815 Scion, 41, 75 Seacrest, Ryan, 52 Seasonal variation, 631, 634–636, 640, 673 Seattle Mariners, 54 Second quartile, 121–122 Seigel, James C., 725, 815 Seinfeld (TV show), 290 Selection bias, 292, 295 Shewhart, Walter, 682–683 Shift parameter, 592 Shiskin, Julius, 646 Sichelman, Lew, 326, 754, 755, 815 Siegel, Andrew F., 815 Sigma level capability, 711–713, 725 Sign test, 734–737, 754 Silk, Alvin J., 309, 815 Simonoff, Jeffrey S., Simple coefficient of determination, 516–519, 543 Simple correlation coefficient, 519–520, 543 Simple exponential smoothing, 647–651 Simple index, 669 Simple linear regression model, 487–490 assumptions, 500–501 confidence intervals, 506, 510–513 definition, 543 distance value, 511 F-test, 522–524 least squares point estimates, 491–496 mean square error, 501–502 point estimation, 496 point prediction, 496 prediction interval, 510–513 regression parameters, 490 residual analysis, 527–534 significance of slope, 503–505 significance of y-intercept, 506 simple coefficient of determination, 516–519 simple correlation coefficient, 519–520 standard error, 501–502 Simpson, O J., 178 Simpson’s paradox, 185 Sincich, Terry, 614 Six sigma capability, 711–713 Six sigma companies, 713 Six sigma philosophy, 713 Skewed to left, 47, 74, 105–106 Skewed to right, 47, 74, 105 Skewness, Empirical Rule and, 116–117 Slope, 130 Slope, of simple linear regression model, 489, 490 confidence interval, 506 definition, 543 least squares point estimates, 492 significance, 503–505 Smith, H., 815 Smith, Ken G., 815 Smoothing constant, 648, 673 Smoothing equation, 648, 650 Southern Wine & Spirits, 142 S&P 500, 124–125 SPAC (sample partial autocorrelation function), 663–667 SPC; see Statistical process control Spearman’s rank correlation coefficient, 521, 750–754, 805 Spielberg, Steven, 52 Spotts, Harlan E., 326, 402, 815 SQC (statistical quality control), 682 Square root transformation, 536 Squared forecast errors, 668 SSB (block sum of squares), 440 SSE; see Error sum of squares SST (treatment sum of squares), 431, 440 SSTO; see Total sum of squares St Louis Cardinals, 54 Stamper, Joseph C., 579 Standard & Poor’s 500 (S&P 500), 124–125 Standard Dermal curve, areas under, 790–791, 805; see also Normal curve Standard deviation binomial random variable, 205 normal distribution, 230 Poisson random variable, 211 population, 111–112 of random variable, 192–193, 218 sample, 112–113 Standard error, 501–502, 511, 566–567, 577 Standard error of the estimate, 314, 334, 503, 572 Standard normal distribution, 232, 259 Standardized normal quartile value, 255–256 Standardized value; see z-scores States of nature, 763, 779 Statesman Journal newspaper, 127 Stationary time series, 660 Statistical acceptance sampling, 682 Statistical analysis, inappropriate, 12 Statistical inference definition, 8, 16 generalizing, 153 for population variance, 414–415 rare event approach, 203 Statistical process control (SPC); see also Control charts causes of variation, 685–687 definition, 725 objectives, 685, 686 Statistical significance, 348 Statistics, Stem-and-leaf displays, 56–57 back-to-back, 58–59 constructing, 57–58 definition, 74 symmetrical, 57 Stems, 56 Stepwise regression, 602–603, 615 Steven Madden, 54 Stevens, Doug L., Stevenson, William J., 767–769, 779–781, 815 Stone, Thomas H., 814 Straight-line relationships; see Linear relationships Strata, 287–288, 295 Stratified random samples, 287–288, 295 Stratified random sampling estimation in, 330–332 sample sizes in, 333–334 Strayer Education, 54 Studentized deleted residuals, 609, 610 Studentized range, percentage points of, 799–800 Studentized residuals, 609, 610 Subaru, 41, 75 Subgroups, 688–689, 700, 725 Subjective probability, 155, 182 Subway, 487 Sum of squared residuals (errors), 492, 542–543, 557 Sums of squares, 431 Surveys, definition, 16 errors, 291–293 bow21493_ind_817-823.qxd 11/30/12 12:14 PM Page 823 www.downloadslide.com 823 Index mail, 291 margins of error, 324–325 nonresponse, 292 personal interviews, 291 phone, 290–291 pilot, 290 questions, 289–290, 293 response rates, 290–291 sample sizes, 290 sampling designs, 287–289 Web-based, 291 Suzuki, 75 Swift, Taylor, 52 Symmetrical distributions, 47, 74, 105, 106 Syntel, 54 Systematic samples, 289, 295 T t distribution, 310–312, 334, 357 t points, 310–312, 334 t table, 310–312, 334, 792–793 t tests, 357–359 Taguchi, Genichi, 685 Taguchi methods, 685 Tampa Bay Rays, 54 Target population, 291–292, 295 Tempur Pedic International, 54 Test statistic, 344, 373 Texas Rangers, 54 Therrien, Lois, 814 Third quartile, 121, 139 Thomas, Anisya S., 815 Thompson, C M., 417, 794–797 3M, 684 Time series data autocorrelation, 531–532 components and models, 631–632, 640 definition, 16, 543, 631, 673 regression assumptions, 501 runs plots, 4, Time series forecasting, 630–673 Box–Jenkins methodology, 660–667 error comparisons, 667–668 Holt–Winters’ double exponential smoothing, 652–660 index numbers, 668–673 multiplicative decomposition, 640–647 seasonal components, 634–637 simple exponential smoothing, 647–652 trend components, 632–634 Time series plots, 4, 5, 16; see also Runs plots Time series regression models, 632 Time Warner Cable, 159n2 Tobacco Institute, 76 Tolerance intervals confidence intervals vs., 315 definition, 114, 139 Empirical Rule and, 114–116, 231 finding with normal table, 244 Toronto Blue Jays, 54 Toronto Raptors, 110 Total quality management (TQM), 683, 725 Total sum of squares (SSTO), 431–432, 440, 447 Total variation, 517–518, 543, 600 Toyota, 40, 41, 75 Toys “R” Us, 142 TQM (total quality management), 683, 725 Transcend Services, 54 TransDigm Group, 54 TransMontaigne Performance Food Group, 142 Travel Industry of America, Treatment mean, 453 Treatment mean square (MST), 432 Treatment sum of squares (SST), 431, 440 Treatments, 427–428, 453 Tree diagrams; see Decision trees Trends, 631–634, 640, 673 Trial control limits, 695, 716 True Religion Apparel, 54 Trump, Donald, 52 Tukey formula, 435 Two-factor factorial experiment, 446–450, 453 Two-sided alternative hypothesis, 343, 370–371, 373 Two standard deviation warning limit, 701 Two-way ANOVA, 445–451 confidence intervals, 450 definition, 453 point estimates, 450 Two-way ANOVA table, 448 Two-way cross-classification table; see Contingency table Type I errors, 344–345, 347, 373 Type II errors, 344–345, 364–371, 373 Tyson Foods, 270 U UCL (upper control limit), 691, 694 UFP Technologies, 54 Unbiased point estimate, 273, 281, 295 Uncertainty, 764–765, 779 Under Armour, 54 Undercoverage, 292, 295 Unexplained variation, 517–518, 543, 600 Unger, L., 10n Uniform distribution, 194, 227–229, 259 Union, of events, 163 Union of Japanese Scientists and Engineers (JUSE), 683 United States Golf Association, 206 U.S Bureau of Labor Statistics, 183, 668, 671 U.S Bureau of the Census, 5, 17, 122, 646, 755 U.S Census Bureau, 5, 17, 160, 646 U.S Commerce Department, 683 U.S Department of Energy, 10 U.S Department of Transportation, 185 U.S Energy Information Administration, U.S War Department, 682 Univariate time series models, 673 University Chrysler/Jeep, 371 Upper control limit (UCL), 691, 694 Upper limit, 123–124 US Foodservice, 142 Utah Jazz, 110 Utilities, 767, 777, 779 Utility curve, 777 Utility theory, 777–778 U2, 52 V VALIC Investment Digest, 78 Values of variables, Variable Annuity Life Insurance Company, 41, 78, 79, 140 Variables, 3, 4, 16; see also Dependent variables; Independent variables; Qualitative variables; Quantitative variables; Random variables Variables, relationships between crosstabulation tables, 61–64 linear, 67, 127 scatter plots, 67–68 Variables control charts, 691, 725 Variance; see also Analysis of variance (ANOVA); Population variance binomial random variable, 205 normal distribution, 230 Poisson random variable, 211 of random variable, 192–193, 218 sample, 112–113, 134–135 of sample mean, 293–294 Variance inflation factors (VIF), 598–600 Variation coefficient of, 117–118 explained, 517–518, 543, 600 measures of, 110–118 in processes, 685–687 total, 517–518, 543, 600 unexplained, 517–518, 543, 600 Venn diagrams, 161 Vertical bar charts, 37 VIF (variance inflation factors), 598–600 VISA, 166, 167, 173 Volkswagen, 75 Volkswagen Group, 41 Voluntary response samples, 270 Voluntary response surveys, 292 Volvo, 75 Von Neumann, J., 777, 815 VSE, 54 W Wainer, Howard, 72 Walsh, Bryan, 11n5, 11n6 Walters, Rockney G., 336, 814 Walton, Mary, 683, 815 Washington Nationals, 54 Washington Post, 406 Washington Wizards, 110 Wasserman, W., 451, 587, 815 Watson, G S., 801, 802 WebMD Health, 54 Weight of evidence, 350 Weighted aggregate price index, 670–671 Weighted mean, 132–133, 139 Weinberger, Daniel R., 184 Weinberger, Marc G., 326, 402, 815 Wendy’s, 510 Western Electric, 682, 700 Western Steakhouses, 541 Westinghouse Electric Corporation, 684 Wheelwright, S C., 540, 646 Whiskers, 123, 656 White Castle, 510 Whitehurst, Kevin, Whole Foods, 316 Wilcox, R A., 803, 804 Wilcoxon, F., 803, 804 Wilcoxon rank sum table, 803 Wilcoxon rank sum test, 388, 738–742, 754 Wilcoxon signed ranks table, 804 Wilcoxon signed ranks test, 395, 744–746, 754 Willingham, John J., 335, 814 Winfrey, Oprah, 52 Winter Olympic Games (19th), 286 Winters’ method, 654–659 Within-treatment variability, 430, 432 Woodruff, Robert B., 579 Woods, D L., 544 Woods, Tiger, 52 Wright, Thomas A., 815 X x-bar charts, 691–699, 725 analyzing, 691–702 center line, 694 constants, 802 control limits, 694 pattern analysis, 700–702 Xerox Corporation, 684 Y y intercept, 130 y intercept, of simple linear regression model, 489, 490 definition, 543 least squares point estimates, 492 significance, 506 Yahoo!, Z z-scores, 117, 139 z tests about population mean, 347–354 about population proportion, 361–364 z values, 232, 240, 259; see also Normal table z␣ point, 240–241, 259 -z␣ point, 242–243, 259 Zogby International, 406 bow21493_ind_case_824.qxd 12/3/12 4:32 PM Page 824 www.downloadslide.com Case Index A G Q Air Conditioner Sales case, 638–639 Air Safety case, 208–210, 253, 316, 320, 360 Auto Insurance case, 381, 391–395, 745–746 Game Show case, 282 Gasoline Additive case, 593–594 Gender Issues at a Pharmaceutical Company, 169–172 Quality Home Improvement Center (QHIC) case, 487, 525–531, 536–538, 619 H Real Estate Sales Price case, 68, 499–500, 503, 508, 509, 516, 521, 525, 561–563, 571, 575, 577–578 B Bank Customer Waiting Time case, 13, 52–53, 60, 61, 108, 119, 120, 271, 282–283, 308, 317, 346, 355, 360, 469 Bike Sales case, 620–621, 634–635 Brokerage Firm case, 35, 61–64, 470–475 C Calculator Sales case, 631, 633–634, 653–655 Camshaft case, 681, 725–728 Car Mileage case, 3, 10–11, 56–58, 102–103, 112–116, 187–188, 225, 237–239, 244, 269, 271–277, 301, 319–320, 465–466 Cardboard Box case, 427, 439, 442–443 Catalyst Comparison case, 381, 383–386, 420–421, 743 CD Player case, 734–737 Cell Phone case, 3, 8–9, 107, 268–269 Cheese Spread case, 250–251, 285, 301, 321–322, 341, 361–363 Cigarette Advertisement case, 336, 374 Cod Catch case, 632–633, 648–652 Coffee Temperature case, 16, 17, 225, 226, 240–241 ColorSmart-5000 case, 203–206 Commercial Loan case, 313, 341, 357–358 Crystal Cable case, 153, 159, 161–164, 167–168 D Department Store case, 331 Direct Labor Cost case, 499, 503, 508, 509, 516, 521, 525 Disk Brake case, 336, 356 DVD case, 241–242 E e-billing case, 35, 42–45, 59–60, 106–107, 113–114, 126, 255–258, 280, 301, 307, 341–343, 360, 469 Electronic Article Surveillance case, 363–364 Electronics World case, 581–586, 751 F Fast-Food Restaurant Rating case, 69, 510 Florida Pool Home case, 142–143, 588–589 Fresh Detergent case, 498–499, 503, 508, 509, 515, 521, 525, 563–565, 571, 575, 578, 590–592, 594–596, 616–618 Hole Location case, 681, 689–690, 694–699, 708–711 Home Theater case, 329–330 Hospital Labor Needs case, 564, 565, 571, 575, 578, 605–608, 611 Hot Chocolate Temperature case, 681, 703–705, 714 I Investment case, 140–142, 260 J Jar Fill case, 418–420 L Laptop Service Time case, 539–541 Life Insurance case, 191 Lumber Production case, 638, 652 M Marketing Ethics case, 322–323, 326–327, 364–365 Marketing Research case, 3, 9–10, 51, 59–60, 106, 126, 269, 314, 469 Microwave Oven case, 462–463 N Natural Gas Consumption case, 68–69, 131–132, 496–497, 502, 507, 514, 521, 524, 561–562, 570–571, 575, 577, 611 O Oil Company case, 427, 428, 433, 435–436, 763, 769–774, 781 Oil Drilling case, 177–179 P Phantol case, 363 Phe-Mycin case, 200–203, 322, 325 R S Sales Invoice case, 716–717 Sales Representative case, 555, 578–580, 600–604, 606 Service Time case, 132, 497, 502, 508, 515, 521, 522, 525, 538–539 Should HIV Testing Be Mandatory? 175–176 Sound City case, 135, 187–194 Standard & Poor’s 500 case, 124–125 Starting Salary case, 497, 502, 507, 508, 514, 521, 522, 525 Stock Return case, 296 Supermarket case, 427–429, 437, 445–446, 450–451, 589–590 T Tasty Cola case, 640–646, 656–659 Tasty Sub Shop case, 487–490, 493–496, 502, 504–506, 512–513, 516–520, 523–524, 542–543, 555–560, 567–570, 574–576, 611 Test Market case, 381, 398, 399, 401 Trash Bag case, 14, 53, 60, 108, 118, 119, 246–247, 296, 308, 317, 341, 342, 360 Traveler’s Rest case, 631, 635–637, 660 V Valentine’s Day Chocolate case, 341, 343, 352, 354, 369–371 Video Game Satisfaction Rating case, 12–13, 52, 60, 108, 119, 270–271, 283, 308, 317, 345–346, 355, 360, 479 W Watch Sales case, 638, 659 bow01838_IBC.qxd 12/11/12 10:05 AM Page www.downloadslide.com A t Table ␣ df 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ЊЊ t␣ t.100 t.050 t.025 t.01 t 005 t 001 t.0005 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576 318.31 22.326 10.213 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.160 3.090 636.62 31.598 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.767 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.373 3.291 bow01838_IBC.qxd 12/11/12 10:05 AM Page www.downloadslide.com A t Table ␣ df 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ЊЊ t␣ t.100 t.050 t.025 t.01 t 005 t 001 t.0005 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576 318.31 22.326 10.213 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.160 3.090 636.62 31.598 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.767 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.373 3.291 bow01838_IBC.qxd 12/11/12 10:05 AM Page www.downloadslide.com Cumulative Areas under the Standard Normal Curve z Cumulative Areas under the Standard Normal Curve (continued) 0 z z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ؊3.9 ؊3.8 ؊3.7 ؊3.6 ؊3.5 ؊3.4 ؊3.3 ؊3.2 ؊3.1 ؊3.0 ؊2.9 ؊2.8 ؊2.7 ؊2.6 ؊2.5 ؊2.4 ؊2.3 ؊2.2 ؊2.1 ؊2.0 ؊1.9 ؊1.8 ؊1.7 ؊1.6 ؊1.5 ؊1.4 ؊1.3 ؊1.2 ؊1.1 ؊1.0 ؊0.9 ؊0.8 ؊0.7 ؊0.6 ؊0.5 ؊0.4 ؊0.3 ؊0.2 ؊0.1 ؊0.0 0.00005 0.00007 0.00011 0.00016 0.00023 0.00034 0.00048 0.00069 0.00097 0.00135 0.0019 0.0026 0.0035 0.0047 0.0062 0.0082 0.0107 0.0139 0.0179 0.0228 0.0287 0.0359 0.0446 0.0548 0.0668 0.0808 0.0968 0.1151 0.1357 0.1587 0.1841 0.2119 0.2420 0.2743 0.3085 0.3446 0.3821 0.4207 0.4602 0.5000 0.00005 0.00007 0.00010 0.00015 0.00022 0.00032 0.00047 0.00066 0.00094 0.00131 0.0018 0.0025 0.0034 0.0045 0.0060 0.0080 0.0104 0.0136 0.0174 0.0222 0.0281 0.0351 0.0436 0.0537 0.0655 0.0793 0.0951 0.1131 0.1335 0.1562 0.1814 0.2090 0.2389 0.2709 0.3050 0.3409 0.3783 0.4168 0.4562 0.4960 0.00004 0.00007 0.00010 0.00015 0.00022 0.00031 0.00045 0.00064 0.00090 0.00126 0.0018 0.0024 0.0033 0.0044 0.0059 0.0078 0.0102 0.0132 0.0170 0.0217 0.0274 0.0344 0.0427 0.0526 0.0643 0.0778 0.0934 0.1112 0.1314 0.1539 0.1788 0.2061 0.2358 0.2676 0.3015 0.3372 0.3745 0.4129 0.4522 0.4920 0.00004 0.00006 0.00010 0.00014 0.00021 0.00030 0.00043 0.00062 0.00087 0.00122 0.0017 0.0023 0.0032 0.0043 0.0057 0.0075 0.0099 0.0129 0.0166 0.0212 0.0268 0.0336 0.0418 0.0516 0.0630 0.0764 0.0918 0.1093 0.1292 0.1515 0.1762 0.2033 0.2327 0.2643 0.2981 0.3336 0.3707 0.4090 0.4483 0.4880 0.00004 0.00006 0.00009 0.00014 0.00020 0.00029 0.00042 0.00060 0.00084 0.00118 0.0016 0.0023 0.0031 0.0041 0.0055 0.0073 0.0096 0.0125 0.0162 0.0207 0.0262 0.0329 0.0409 0.0505 0.0618 0.0749 0.0901 0.1075 0.1271 0.1492 0.1736 0.2005 0.2296 0.2611 0.2946 0.3300 0.3669 0.4052 0.4443 0.4840 0.00004 0.00006 0.00009 0.00013 0.00019 0.00028 0.00040 0.00058 0.00082 0.00114 0.0016 0.0022 0.0030 0.0040 0.0054 0.0071 0.0094 0.0122 0.0158 0.0202 0.0256 0.0322 0.0401 0.0495 0.0606 0.0735 0.0885 0.1056 0.1251 0.1469 0.1711 0.1977 0.2266 0.2578 0.2912 0.3264 0.3632 0.4013 0.4404 0.4801 0.00004 0.00006 0.00008 0.00013 0.00019 0.00027 0.00039 0.00056 0.00079 0.00111 0.0015 0.0021 0.0029 0.0039 0.0052 0.0069 0.0091 0.0119 0.0154 0.0197 0.0250 0.0314 0.0392 0.0485 0.0594 0.0721 0.0869 0.1038 0.1230 0.1446 0.1685 0.1949 0.2236 0.2546 0.2877 0.3228 0.3594 0.3974 0.4364 0.4761 0.00004 0.00005 0.00008 0.00012 0.00018 0.00026 0.00038 0.00054 0.00076 0.00107 0.0015 0.0021 0.0028 0.0038 0.0051 0.0068 0.0089 0.0116 0.0150 0.0192 0.0244 0.0307 0.0384 0.0475 0.0582 0.0708 0.0853 0.1020 0.1210 0.1423 0.1660 0.1922 0.2206 0.2514 0.2843 0.3192 0.3557 0.3936 0.4325 0.4721 0.00003 0.00005 0.00008 0.00012 0.00017 0.00025 0.00036 0.00052 0.00074 0.00103 0.0014 0.0020 0.0027 0.0037 0.0049 0.0066 0.0087 0.0113 0.0146 0.0188 0.0239 0.0301 0.0375 0.0465 0.0571 0.0694 0.0838 0.1003 0.1190 0.1401 0.1635 0.1894 0.2177 0.2482 0.2810 0.3156 0.3520 0.3897 0.4286 0.4681 0.00003 0.00005 0.00008 0.00011 0.00017 0.00024 0.00035 0.00050 0.00071 0.00100 0.0014 0.0019 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0367 0.0455 0.0559 0.0681 0.0823 0.0985 0.1170 0.1379 0.1611 0.1867 0.2148 0.2451 0.2776 0.3121 0.3483 0.3859 0.4247 0.4641 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.99865 0.99903 0.99931 0.99952 0.99966 0.99977 0.99984 0.99989 0.99993 0.99995 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.99869 0.99906 0.99934 0.99953 0.99968 0.99978 0.99985 0.99990 0.99993 0.99995 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.99874 0.99910 0.99936 0.99955 0.99969 0.99978 0.99985 0.99990 0.99993 0.99996 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.99878 0.99913 0.99938 0.99957 0.99970 0.99979 0.99986 0.99990 0.99994 0.99996 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.99882 0.99916 0.99940 0.99958 0.99971 0.99980 0.99986 0.99991 0.99994 0.99996 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.99886 0.99918 0.99942 0.99960 0.99972 0.99981 0.99987 0.99991 0.99994 0.99996 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.99889 0.99921 0.99944 0.99961 0.99973 0.99981 0.99987 0.99992 0.99994 0.99996 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.99893 0.99924 0.99946 0.99962 0.99974 0.99982 0.99988 0.99992 0.99995 0.99996 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7518 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.99897 0.99926 0.99948 0.99964 0.99975 0.99983 0.99988 0.99992 0.99995 0.99997 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.99900 0.99929 0.99950 0.99965 0.99976 0.99983 0.99989 0.99992 0.99995 0.99997 bow01838_IBC.qxd 12/11/12 10:05 AM Page www.downloadslide.com Cumulative Areas under the Standard Normal Curve z Cumulative Areas under the Standard Normal Curve (continued) 0 z z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ؊3.9 ؊3.8 ؊3.7 ؊3.6 ؊3.5 ؊3.4 ؊3.3 ؊3.2 ؊3.1 ؊3.0 ؊2.9 ؊2.8 ؊2.7 ؊2.6 ؊2.5 ؊2.4 ؊2.3 ؊2.2 ؊2.1 ؊2.0 ؊1.9 ؊1.8 ؊1.7 ؊1.6 ؊1.5 ؊1.4 ؊1.3 ؊1.2 ؊1.1 ؊1.0 ؊0.9 ؊0.8 ؊0.7 ؊0.6 ؊0.5 ؊0.4 ؊0.3 ؊0.2 ؊0.1 ؊0.0 0.00005 0.00007 0.00011 0.00016 0.00023 0.00034 0.00048 0.00069 0.00097 0.00135 0.0019 0.0026 0.0035 0.0047 0.0062 0.0082 0.0107 0.0139 0.0179 0.0228 0.0287 0.0359 0.0446 0.0548 0.0668 0.0808 0.0968 0.1151 0.1357 0.1587 0.1841 0.2119 0.2420 0.2743 0.3085 0.3446 0.3821 0.4207 0.4602 0.5000 0.00005 0.00007 0.00010 0.00015 0.00022 0.00032 0.00047 0.00066 0.00094 0.00131 0.0018 0.0025 0.0034 0.0045 0.0060 0.0080 0.0104 0.0136 0.0174 0.0222 0.0281 0.0351 0.0436 0.0537 0.0655 0.0793 0.0951 0.1131 0.1335 0.1562 0.1814 0.2090 0.2389 0.2709 0.3050 0.3409 0.3783 0.4168 0.4562 0.4960 0.00004 0.00007 0.00010 0.00015 0.00022 0.00031 0.00045 0.00064 0.00090 0.00126 0.0018 0.0024 0.0033 0.0044 0.0059 0.0078 0.0102 0.0132 0.0170 0.0217 0.0274 0.0344 0.0427 0.0526 0.0643 0.0778 0.0934 0.1112 0.1314 0.1539 0.1788 0.2061 0.2358 0.2676 0.3015 0.3372 0.3745 0.4129 0.4522 0.4920 0.00004 0.00006 0.00010 0.00014 0.00021 0.00030 0.00043 0.00062 0.00087 0.00122 0.0017 0.0023 0.0032 0.0043 0.0057 0.0075 0.0099 0.0129 0.0166 0.0212 0.0268 0.0336 0.0418 0.0516 0.0630 0.0764 0.0918 0.1093 0.1292 0.1515 0.1762 0.2033 0.2327 0.2643 0.2981 0.3336 0.3707 0.4090 0.4483 0.4880 0.00004 0.00006 0.00009 0.00014 0.00020 0.00029 0.00042 0.00060 0.00084 0.00118 0.0016 0.0023 0.0031 0.0041 0.0055 0.0073 0.0096 0.0125 0.0162 0.0207 0.0262 0.0329 0.0409 0.0505 0.0618 0.0749 0.0901 0.1075 0.1271 0.1492 0.1736 0.2005 0.2296 0.2611 0.2946 0.3300 0.3669 0.4052 0.4443 0.4840 0.00004 0.00006 0.00009 0.00013 0.00019 0.00028 0.00040 0.00058 0.00082 0.00114 0.0016 0.0022 0.0030 0.0040 0.0054 0.0071 0.0094 0.0122 0.0158 0.0202 0.0256 0.0322 0.0401 0.0495 0.0606 0.0735 0.0885 0.1056 0.1251 0.1469 0.1711 0.1977 0.2266 0.2578 0.2912 0.3264 0.3632 0.4013 0.4404 0.4801 0.00004 0.00006 0.00008 0.00013 0.00019 0.00027 0.00039 0.00056 0.00079 0.00111 0.0015 0.0021 0.0029 0.0039 0.0052 0.0069 0.0091 0.0119 0.0154 0.0197 0.0250 0.0314 0.0392 0.0485 0.0594 0.0721 0.0869 0.1038 0.1230 0.1446 0.1685 0.1949 0.2236 0.2546 0.2877 0.3228 0.3594 0.3974 0.4364 0.4761 0.00004 0.00005 0.00008 0.00012 0.00018 0.00026 0.00038 0.00054 0.00076 0.00107 0.0015 0.0021 0.0028 0.0038 0.0051 0.0068 0.0089 0.0116 0.0150 0.0192 0.0244 0.0307 0.0384 0.0475 0.0582 0.0708 0.0853 0.1020 0.1210 0.1423 0.1660 0.1922 0.2206 0.2514 0.2843 0.3192 0.3557 0.3936 0.4325 0.4721 0.00003 0.00005 0.00008 0.00012 0.00017 0.00025 0.00036 0.00052 0.00074 0.00103 0.0014 0.0020 0.0027 0.0037 0.0049 0.0066 0.0087 0.0113 0.0146 0.0188 0.0239 0.0301 0.0375 0.0465 0.0571 0.0694 0.0838 0.1003 0.1190 0.1401 0.1635 0.1894 0.2177 0.2482 0.2810 0.3156 0.3520 0.3897 0.4286 0.4681 0.00003 0.00005 0.00008 0.00011 0.00017 0.00024 0.00035 0.00050 0.00071 0.00100 0.0014 0.0019 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0367 0.0455 0.0559 0.0681 0.0823 0.0985 0.1170 0.1379 0.1611 0.1867 0.2148 0.2451 0.2776 0.3121 0.3483 0.3859 0.4247 0.4641 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.99865 0.99903 0.99931 0.99952 0.99966 0.99977 0.99984 0.99989 0.99993 0.99995 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.99869 0.99906 0.99934 0.99953 0.99968 0.99978 0.99985 0.99990 0.99993 0.99995 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.99874 0.99910 0.99936 0.99955 0.99969 0.99978 0.99985 0.99990 0.99993 0.99996 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.99878 0.99913 0.99938 0.99957 0.99970 0.99979 0.99986 0.99990 0.99994 0.99996 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.99882 0.99916 0.99940 0.99958 0.99971 0.99980 0.99986 0.99991 0.99994 0.99996 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.99886 0.99918 0.99942 0.99960 0.99972 0.99981 0.99987 0.99991 0.99994 0.99996 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.99889 0.99921 0.99944 0.99961 0.99973 0.99981 0.99987 0.99992 0.99994 0.99996 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.99893 0.99924 0.99946 0.99962 0.99974 0.99982 0.99988 0.99992 0.99995 0.99996 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7518 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.99897 0.99926 0.99948 0.99964 0.99975 0.99983 0.99988 0.99992 0.99995 0.99997 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.99900 0.99929 0.99950 0.99965 0.99976 0.99983 0.99989 0.99992 0.99995 0.99997 www.downloadslide.com The Seventh Edition of Business Statistics in Practice presents accurate statistical content in an engaging and relevant manner This edition offers improved topic flow and the use of realistic and compelling business examples, while covering all previous edition material and several new topics with eighty fewer pages 7e Features of the seventh edition: the margins and performing hypothesis tests instructions in the end of chapter material McGraw-Hill Connect® Business Statistics, an online assignment and assessment tool, connects students with the resources they need for success in the course Business Statistics in Practice This approach helps to alleviate student anxiety in learning new concepts and enhances overall comprehension Bowerman O’Connell Murphree ISBN 978-0-07-352149-7 MHID 0-07-352149-3 EAN www.mhhe.com Business Statistics in Practice Bruce L Bowerman Richard T O’Connell Emily S Murphree Md Dalim #1216885 11/27/12 Cyan Mag Yelo Black To learn more about the resources available to you, visit www.mhhe.com/bowerman7e 7e ... DS ShopExp 124 $119 .25 $ 123 .71 $ 121 . 32 $ 121 . 72 $ 122 .34 $ 122 . 42 $ 120 .14 $ 123 .63 $ 122 .19 $ 122 .44 $114.88 $115.38 $115.11 $114.40 $117. 02 $113.91 $116.89 $111.87 Albert’s $111.99 $116. 62 Expense Miller’s... follows that sx1Ϫx2 ϭ s21 s2 s2 s2 1 ϩ 2 ϩ ϭ s2 ϩ B n1 n2 B n1 n2 B n1 n2 Because we are assuming that s21 ϭ s 22 ϭ s , we not need separate estimates of s21 and s 22 Instead, we combine the results... for m1 Ϫ m2 is B( x Ϫ x 2) Ϯ t 025 df ϭ 025 B s2p n R n2 ϭ B(811 Ϫ 750 .2) Ϯ 2. 306 025 95 Ϫt. 025 ϩ B 435.1 5 ϩ 5 R 1 ϭ [60.8 Ϯ 30. 421 7] ϭ [30.38, 91 .22 ] t. 025 2. 306 Here t. 025 ϭ 2. 306 is based