CH 10 inference about means and proportions with two populations XSTK

CH 10 - Inference About Means and Proportions with Two Populations Multiple Choice If we are interested in testing whether the proportion of items in population is larger than the proportion of items in population 2, the a null hypothesis should state p1 - p2 < b null hypothesis should state p1 - p2 > c alternative hypothesis should state p1 - p2 > d alternative hypothesis should state p1 - p2 < ANSWER: c POINTS: DIFFICULTY: Easy LEARNING OBJECTI BSST.ASWC.17.10.04 - Inferences About the Difference Between Two VES: Population Proportions NATIONAL STANDA United States - BUSPROG: Analytic RDS: STATE STANDARDS: United States - AK - DISC: Hypothesis Testing Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations KEYWORDS: Bloom's: Understand To compute an interval estimate for the difference between the means of two populations, the t distribution a is restricted to small sample situations b is not restricted to small sample situations c can be applied when the populations have equal means d can be applied only when the populations have equal standard deviations ANSWER: b POINTS: DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Interval Estimation S: Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations KEYWORDS: Bloom's: Understand When developing an interval estimate for the difference between two population means with sample sizes of n1 and n2, a n1 must be equal to n2 b n1 must be smaller than n2 c n1 must be larger than n2 d n1 and n2 can be of different sizes ANSWER: d POINTS: DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Interval Estimation S: Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations KEYWORDS: Bloom's: Understand To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample and n2 the size of sample 2) a (n1 + n2) degrees of freedom b (n1 + n2 - 1) degrees of freedom c (n1 + n2 - 2) degrees of freedom d (n1 - n2 + 2) degrees of freedom ANSWER: c POINTS: DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Interval Estimation Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations S: KEYWORDS: Bloom's: Remember When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a corresponding samples b matched samples c independent samples d pooled samples ANSWER: b POINTS: DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.03 - Inferences About the Difference Between Two CTIVES: Population Means: Matched Samples NATIONAL STAND United States - BUSPROG: Analytic ARDS: Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations STATE STANDARD United States - AK - DISC: Statistical Inference S: KEYWORDS: Bloom's: Remember Two independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal The sample sizes are n1 = 32 and n2 = 40 The correct distribution to use is the a t distribution with 73 degrees of freedom b t distribution with 72 degrees of freedom c t distribution with 71 degrees of freedom d t distribution with 70 degrees of freedom ANSWER: d POINTS: DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Hypothesis Testing S: KEYWORDS: Bloom's: Apply Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal The sample sizes are n1 = 25 and n2 = 35 The correct distribution to use is the a t distribution with 61 degrees of freedom b t distribution with 60 degrees of freedom c t distribution with 59 degrees of freedom d t distribution with 58 degrees of freedom ANSWER: d POINTS: DIFFICULTY: Easy Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Hypothesis Testing S: KEYWORDS: Bloom's: Apply If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a can be approximated by any distribution b will have a variance of one c can be approximated by a normal distribution d will have a mean of one ANSWER: c POINTS: DIFFICULTY: Easy Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations LEARNING OBJE BSST.ASWC.17.10.01 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Known NATIONAL STAND United States - BUSPROG: Analytic ARDS: STATE STANDARD United States - AK - DISC: Statistical Inference S: KEYWORDS: Bloom's: Remember The standard error of - is the a pooled estimator of - b variance of the sampling distribution of - c standard deviation of the sampling distribution of d margin of error of ANSWER: c POINTS: - - Copyright Cengage Learning Powered by Cognero Page CH 10 - Inference About Means and Proportions with Two Populations DIFFICULTY: Easy LEARNING OBJE BSST.ASWC.17.10.01 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Known NATIONAL STAND United States - BUSPROG: Analytic ARDS: STATE STANDARD United States - AK - DISC: Statistical Inference S: KEYWORDS: Bloom's: Remember 10 The sampling distribution of - is approximated by a a normal distribution b t distribution with n1 + n2 degrees of freedom c t distribution with n1 + n2 - degrees of freedom d - distribution ANSWER: a POINTS: Copyright Cengage Learning Powered by Cognero Page 10 CH 10 - Inference About Means and Proportions with Two Populations 111 The reliability of two types of machines used in the same manufacturing process is to be tested The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials a Give a point estimate of the difference between the population proportions of these machines b Calculate the pooled estimate of the population proportion c Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a 10 level of significance ANSWER: a .10 b .2545 c test statistic z = 2.68, p-value = 0074, reject H0; there is a statistically significant difference in the reliability for the two types of machines POINTS: DIFFICULTY: Challenging LEARNING OBJECT BSST.ASWC.17.10.04 - Inferences About the Difference Between Two IVES: Population Proportions NATIONAL STANDA United States - BUSPROG: Analytic RDS: Copyright Cengage Learning Powered by Cognero Page 152 CH 10 - Inference About Means and Proportions with Two Populations STATE STANDARDS United States - AK - DISC: Hypothesis Testing : United States - AK - DISC: Statistical Inference KEYWORDS: Bloom's: Apply | Bloom's: Understand 112 A company attempts to evaluate the potential for a new bonus plan and decides to use the bonus plan for a trial period The weekly sales volume achieved by a sample of salespersons before and after implementing the bonus plan is shown below (For the following matched samples, let the difference d = After - Before.) Weekly Sales (in units) Salesperson Before After 48 44 48 40 38 36 44 50 Assume the population of differences is normally distributed a State the hypotheses b Compute the test statistic Copyright Cengage Learning Powered by Cognero Page 153 CH 10 - Inference About Means and Proportions with Two Populations c Use α = 05 and test to see if the bonus plan will result in an increase in the mean weekly sales for the company ANSWER: a H0: μd ≤ Ha: μd > b t = -.679 p-value (.2729) > 2, not reject H0; there is no sufficient evidence to c conclude that the bonus plan will result in an increase in the mean weekly sales POINTS: DIFFICULTY: Moderate LEARNING OBJE BSST.ASWC.17.10.03 - Inferences About the Difference Between Two CTIVES: Population Means: Matched Samples NATIONAL STAND United States - BUSPROG: Analytic ARDS: STATE STANDARD United States - AK - DISC: Hypothesis Testing S: KEYWORDS: Bloom's: Apply | Bloom's: Understand Copyright Cengage Learning Powered by Cognero Page 154 CH 10 - Inference About Means and Proportions with Two Populations 113 The following information was obtained from matched samples regarding the productivity (in units per hour) of four individuals using two different methods of production Individual Method Method 7 5 6 Let d = Method - Method Is there a significant difference between the mean productivity of the two methods? Let α = 05 Assume the population of differences is normally distributed ANSWER: H0: μd = Ha: μd ≠ Copyright Cengage Learning Powered by Cognero Page 155 CH 10 - Inference About Means and Proportions with Two Populations Test statistic t = 2.542, p-value (.044) is between 02 and 05; reject H0; there is a significant difference between the productivity of the two methods POINTS: DIFFICULTY: Moderate LEARNING O BSST.ASWC.17.10.03 - Inferences About the Difference Between Two BJECTIVES: Population Means: Matched Samples NATIONAL ST United States - BUSPROG: Analytic ANDARDS: STATE STAND United States - AK - DISC: Hypothesis Testing ARDS: KEYWORDS: Bloom's: Apply | Bloom's: Understand 114 The results of a recent poll on the preference of voters regarding presidential candidates are shown below Candidate Voters Surveyed Voters Favoring This Candidate A 400 192 B 450 225 Copyright Cengage Learning Powered by Cognero Page 156 CH 10 - Inference About Means and Proportions with Two Populations Using α = 05, test to determine whether or not there is a significant difference between the preferences for the two candidates ANSWER: H0: pA - pB = Ha: pA - pB ≠ z = -.58; p-value = 562; not reject H0; it cannot be concluded that there is a significant difference between the preferences POINTS: DIFFICULTY: Moderate LEARNING OBJ BSST.ASWC.17.10.04 - Inferences About the Difference Between Two ECTIVES: Population Proportions NATIONAL STA United States - BUSPROG: Analytic NDARDS: STATE STANDA United States - AK - DISC: Hypothesis Testing RDS: Copyright Cengage Learning Powered by Cognero Page 157 CH 10 - Inference About Means and Proportions with Two Populations KEYWORDS: Bloom's: Apply | Bloom's: Understand 115 A potential investor conducted a 49-day survey in each of the North Mall and South Mall theaters in order to determine the difference between the average daily attendance at these two theaters The North Mall theater averaged 720 patrons per day with a variance of 100; while the South Mall theater averaged 700 patrons per day with a variance of 96 Develop an interval estimate for the difference between the average daily attendance at the two theaters Use a confidence coefficient of 95 ANSWER: 16.03 to 23.97 rounding 16 to 24 POINTS: DIFFICULTY: Challenging LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Interval Estimation S: KEYWORDS: Bloom's: Apply 116 From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items Determine a 95% confidence interval estimate for the difference between the proportion of defectives in the two Copyright Cengage Learning Powered by Cognero Page 158 CH 10 - Inference About Means and Proportions with Two Populations lines ANSWER: -.01 to 05 POINTS: DIFFICULTY: Moderate LEARNING OBJECTI BSST.ASWC.17.10.04 - Inferences About the Difference Between Two VES: Population Proportions NATIONAL STANDA United States - BUSPROG: Analytic RDS: STATE STANDARDS: United States - AK - DISC: Interval Estimation KEYWORDS: Bloom's: Apply 117 Two independent samples are drawn from two populations, and the following information is provided n s Sample Sample 34 52 55 65 14 18 Copyright Cengage Learning Powered by Cognero Page 159 CH 10 - Inference About Means and Proportions with Two Populations We want to test the following hypotheses H0: μ1 - μ2 ≥ Ha: μ1 - μ2 < a Determine the degrees of freedom b Compute the test statistic c At the 5% level, test the hypotheses Assume the two populations are normally distributed and have equal variances ANSWER: a 81 b t = -2.887 c p-value (.0025) < 005, reject H0 POINTS: Copyright Cengage Learning Powered by Cognero Page 160 CH 10 - Inference About Means and Proportions with Two Populations DIFFICULTY: Challenging LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Hypothesis Testing S: United States - AK - DISC: Statistical Inference KEYWORDS: Bloom's: Apply | Bloom's: Understand 118 In order to estimate the difference between the average yearly salaries of top managers in private and governmental organizations, the following information was gathered Private Governmental Sample Size 50 60 Sample Mean (in $1000s) 90 80 Sample Standard Deviation (in $1000s) Develop an interval estimate for the difference between the average yearly salaries of top managers of the two sectors Copyright Cengage Learning Powered by Cognero Page 161 CH 10 - Inference About Means and Proportions with Two Populations Use 95% confidence and give your answers in dollars ANSWER: $7380 to $12,620 POINTS: DIFFICULTY: Challenging LEARNING OBJE BSST.ASWC.17.10.02 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Unknown NATIONAL STAN United States - BUSPROG: Analytic DARDS: STATE STANDARD United States - AK - DISC: Interval Estimation S: KEYWORDS: Bloom's: Apply 119 Independent random samples taken at two companies provided the following information regarding annual salaries of the employees The population standard deviations are also given below Company A Company B Sample Size 72 50 Sample Mean (in $1000) 48 43 Copyright Cengage Learning Powered by Cognero Page 162 CH 10 - Inference About Means and Proportions with Two Populations Population Standard Deviation (in $1000) a 12 10 salaries of the employees at the two companies Compute the test statistic ANSWER: a test statistic z = 2.5 b p-value = 0124 < 05, thus, reject H0 and conclude there is a significant difference in the average salaries POINTS: DIFFICULTY: Moderate LEARNING OBJE BSST.ASWC.17.10.01 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Known NATIONAL STAND United States - BUSPROG: Analytic ARDS: STATE STANDARD United States - AK - DISC: Hypothesis Testing S: KEYWORDS: Bloom's: Apply | Bloom's: Understand Copyright Cengage Learning Powered by Cognero Page 163 CH 10 - Inference About Means and Proportions with Two Populations 120 A poll was taken this year asking college students if they considered themselves overweight A similar poll was taken five years ago Results are summarized below Has the proportion increased significantly? Let α = 05 Sample Size Number Considered Themselves Overweight Present Sample 300 150 Previous sample 275 121 ANSWER: H0: p1 - p2 ≤ Ha: p1 - p2 > z = 1.44; p-value = 0749; not reject H0; there is no sufficient evidence to conclude that the proportion has increased significantly POINTS: DIFFICULTY: Moderate LEARNING OBJ BSST.ASWC.17.10.04 - Inferences About the Difference Between Two ECTIVES: Population Proportions NATIONAL STA United States - BUSPROG: Analytic NDARDS: Copyright Cengage Learning Powered by Cognero Page 164 CH 10 - Inference About Means and Proportions with Two Populations STATE STANDA United States - AK - DISC: Hypothesis Testing RDS: KEYWORDS: Bloom's: Apply | Bloom's: Understand 121 Babies weighing less than 5.5 pounds at birth are considered “low-birth-weight babies.” In the United States, 7.6% of newborns are low-birth-weight babies The following information was accumulated from samples of new births taken from two counties Hamilton Shelby Sample size 150 200 Number of low-birth-weight babies 18 22 a Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties b Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of part (a) Do not perform any test ANSWER: a -.0577 to 0777 Because the range of the interval is from negative to positive, there is b no indication that one proportion is significantly different (at 95% confidence) from the other Copyright Cengage Learning Powered by Cognero Page 165 CH 10 - Inference About Means and Proportions with Two Populations POINTS: DIFFICULTY: Moderate LEARNING OBJECT BSST.ASWC.17.10.04 - Inferences About the Difference Between Two IVES: Population Proportions NATIONAL STANDA United States - BUSPROG: Analytic RDS: STATE STANDARDS United States - AK - DISC: Interval Estimation : KEYWORDS: Bloom's: Apply | Bloom's: Understand Copyright Cengage Learning Powered by Cognero Page 166 ... Cognero Page CH 10 - Inference About Means and Proportions with Two Populations LEARNING OBJE BSST.ASWC.17 .10. 01 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Known... Page 27 CH 10 - Inference About Means and Proportions with Two Populations LEARNING OBJE BSST.ASWC.17 .10. 01 - Inferences About the Difference Between Two CTIVES: Population Means: σ1 and σ2 Known... Page 45 CH 10 - Inference About Means and Proportions with Two Populations LEARNING OBJE BSST.ASWC.17 .10. 03 - Inferences About the Difference Between Two CTIVES: Population Means: Matched Samples