BÀI TẬP: 1,1 Số anh chị em. Giáo sư Weiss đã thống kê: hỏi các sinh viên của mình cho biết họ có bao nhiêu anh chị em. Các câu trả lời được thể hiện trong bảng sau. Sử dụng nhóm đơn giá trị.??? 1 3 2 1 1 0 1 1 3 0 2 2 1 2 0 2 1 2 2 1 0 1 1 1 1 1 0 2 0 3 4 2 0 2 1 1 2 1 1 0 3.1 Tiêu thụ pho mát. Bộ Nông nghiệp Hoa Kỳ báo cáo về tiêu dùng, giá cả và chi tiêu mà người tiêu dùng Mỹ tiêu thụ khoảng 32 lb pho mát trong năm 2007. Mức tiêu thụ pho mát đã tăng lên đều đặn từ năm 1960, khi người Mỹ trung bình chỉ ăn 8,3 lb pho mát mỗi năm. Bảng sau đây cung cấp mức tiêu thụ pho mát năm ngoái, tính bằng cân Anh, cho 35 người Mỹ chọn lọc ngẫu nhiên. Sử dụng nhóm giới hạn với một lớp đầu tiên từ 2022 và chiều rộng của lớp là
Trang 1Bài tập
1.1 Number of Siblings Professor Weiss asked his introductory statistics
students to state how many siblings they have The responses are shown in thefollowing table Use single-value grouping
3.1 Cheese Consumption The U.S Department of Agriculture reports in Food
Consumption, Prices, and Expenditures that the average American consumedabout 32 lb of cheese in 2007 Cheese consumption has increased steadily since
1960, when the average American ate only 8.3 lb of cheese annually Thefollowing table provides last year’s cheese consumption, in pounds, for 35randomly selected Americans Use limit grouping with a first class of 20–22 and aclass width of 3
3.2 Top Broadcast Shows The viewing audiences, in millions, for the top 20
television shows, as determined by the Nielsen Ratings for the week endingOctober 26, 2008, are shown in the following table Use cutpoint grouping with afirst class of 12–under 13
19.492 18.497 17.226 16.350 15.953
15.479 15.282 15.012 14.634 14.630
14.451 14.390 13.505 13.309 13.277
13.085 13.059 12.816 12.777 12.257
3.3 Top Recording Artists From the Recording Industry Association of America
Web site, we obtained data on the number of albums sold, in millions, for the toprecording artists (U.S sales only) as of November 6, 2008 Those data areprovided on the WeissStats CD Use the technology of your choice to
a obtain frequency and relative-frequency distributions
b get and interpret a frequency histogram or a relative-frequency histogram
Trang 2c construct a dotplot
d Compare your graphs from parts (b) and (c) (Ex.2.76)
3.4 Educational Attainment As reported by the U.S Census Bureau in Current
Population Reports, the percentage of adults in each state and the District ofColumbia who have completed high school is provided on the WeissStats CD.Apply the technology of your choice to construct a stem-and-leaf diagram of thepercentages with a one line per stem b two lines per stem c five lines perstem d Which stem-and-leaf diagram do you consider most useful? Explain youranswer ) (Ex.2.77)
3.5 Body Temperature A study by researchers at the University of Maryland
addressed the question of whether the mean body temperature of humans is98.6◦F The results of the study by P Mackowiak et al appeared in the article “ACritical Appraisal of 98.6◦F, the Upper Limit of the Normal Body Temperature,and Other Legacies of Carl Reinhold August Wunderlich” (Journal of the AmericanMedical Association, Vol 268, pp 1578–1580) Among other data, theresearchers obtained the body tempera- tures of 93 healthy humans, as provided
on the WeissStats CD Use the technology of your choice to obtain and interpret
a a frequency histogram or a relative-frequency histogram of the temperatures
b a dotplot of the temperatures
c a stem-and-leaf diagram of the temperatures
d Compare your graphs from parts (a)–(c) Which do you find most useful?
(Ex.2.79)
3.6 Weights of 18- to 24-Year-Old Males Refer to the weight data in Table 2.8 onpage 53 Note that there are 37 observations, the smallest and largest of whichare 129.2 and 278.8, respectively Apply the preceding procedure to chooseclasses for cutpoint grouping Use approximately eight classes Note: If in Step 2you decide on 20 for the class width and in Step 3 you choose 120 for the lowercutpoint of the first class, then you will get the same classes as used in Example2.14; otherwise, you will get different classes (which is fine) (Ex.2.82)
3.7 Contents of Soft Drinks A soft-drink bottler fills bottles with soda For qualityassurance purposes, filled bottles are sam- pled to ensure that they contain close
to the content indicated on the label A sample of 30 “one-liter” bottles of sodacontain the amounts, in milliliters, shown in following table Construct a stem-and-leaf diagram for these data (Ex.2.68)
3.8 Explain the meaning of
a distribution of a data set b sample data c population data d census data e.sample distribution f population distribution g distribution of a variable
3.9 Give two reasons why the use of smooth curves to describe shapes ofdistributions is helpful
3.10 Suppose that a variable of a population has a bell-shaped distribution If youtake a large simple random sample from the population, roughly what shapewould you expect the distribution of the sample to be? Explain your answer
Trang 33.11 Identify and sketch three distribution shapes that are symmetric.
3.12 U.S Divisions The U.S Census Bureau divides the states in the UnitedStates into nine divisions: East North Central (ENC), East South Central (ESC),Middle Atlantic (MAC), Moun- tain (MTN), New England (NED), Pacific (PAC), SouthAtlantic (SAC), West North Central (WNC), and West South Central (WSC) Thefollowing table gives the divisions of each of the 50 states
ESC PAC MTN WSC PAC MTN NED SAC SAC SAC
PAC MTN ENC ENC WNC WNC ESC WSC NED SAC
NED ENC WNC ESC WNC MTN WNC MTN NED MAC
MTN MAC SAC WNC ENC WSC PAC MAC NED SAC
WNC ESC WSC MTN NED SAC PAC SAC ENC MTN
a Identify the population and variable under consideration b Obtain both afrequency distribution and a relative-frequency distribution of the divisions c.Draw a pie chart of the divisions d Construct a bar chart of the divisions e.Interpret your results
Chương 3
Mục tiêu:
1 use and understand the formulas in this chapter
2 explain the purpose of a measure of center
3 obtain and interpret the mean, the median, and the mode(s) of a data set
4 choose an appropriate measure of center for a data set
5 use and understand summation notation
6 define, compute, and interpret a sample mean
7 explain the purpose of a measure of variation
8 define, compute, and interpret the range of a data set
9 define, compute, and interpret a sample standard deviation
10 define percentiles, deciles, and quartiles
11 obtain and interpret the quartiles, IQR, and five-number sum- mary of a dataset
12 obtain the lower and upper limits of a data set and identify potential outliers
13 construct and interpret a boxplot
14 use boxplots to compare two or more data sets
15 use a boxplot to identify distribution shape for large data sets
16 define the population mean (mean of a variable)
17 define the population standard deviation (standard deviation of a variable)
18 compute the population mean and population standard devi- ation of a finitepopulation
Trang 419 distinguish between a parameter and a statistic.
20 understand how and why statistics are used to estimate parameters
21 define and obtain standardized variables
22 obtain and interpret z-scores
Bài tập
3.1 Explain in detail the purpose of a measure of center
3.2 Name and describe the three most important measures of center
3.3 Of the mean, median, and mode, which is the only one appropriate for usewith qualitative data?
3.4 True or false: The mean, median, and mode can all be used with quantitativedata Explain your answer
3.5 For a particular population, is the population mean a variable? What about asample mean?
The following table displays a set of scores for a 40-question algebra final exam
2 15 16 16 19 21 21 25 26 27
4 15 16 17 20 21 24 25 27 28
a Do any of the scores look like outliers? b Compute the usual mean of the data
c Compute the 5% trimmed mean of the data d Compute the 10% trimmedmean of the data e Compare the means you obtained in parts (b)–(d) Which ofthe three means provides the best measure of center for the data?
3.6 Explain the purpose of a measure of variation
3.7 Why is the standard deviation preferable to the range as a measure ofvariation?
3.8 Consider the following four data sets
3.9 The following table contains two data sets Data Set II was obtained byremoving the outliers from Data Set I
Trang 5Data Set I Data Set II
on variation? Explain your answer
3.10 Days to Maturity The first two columns of the following table provide a
frequency distribution, using limit grouping, for the days to maturity of 40 term investments, as found in BARRON’S The third column shows the classmarks
short-Days to maturity Frequency f Class mark x
3.11 Identify an advantage that the median and interquartile range have overthe mean and standard deviation, respectively
3.12 Is an extreme observation necessarily an outlier? Explain your answer
3.13 Nicotine Patches In the paper “The Smoking Cessation Efficacy of Varying
Doses of Nicotine Patch Delivery Systems 4 to 5 Years Post-Quit Day”(Preventative Medicine, 28, pp 113–118), D Daughton et al discussed the long-term effectiveness of transdermal nicotine patches on participants who hadpreviously smoked at least 20 cigarettes per day A sample of 15 participants inthe Transdermal Nicotine Study Group (TNSG) reported that they now smoke thefollowing number of cigarettes per day
Trang 69 10 8 8 10
a Determine the quartiles for these data b Remark on the usefulness ofquartiles with respect to this data set
3.14 Dallas Mavericks From the ESPN Web site, in theDallas Mavericks Roster,
we obtained the following weights, in pounds, for the players on that basketballteam for the 2008– 2009 season
175 240 265 280 235 200 210
210 245 230 218 180 225 215
Obtain the following parameters for these weights Use the appropriatemathematical notation for the parameters to express your answers a Mean b.Standard deviation c Median d Mode e IQR
4.2 Which of the following numbers could not possibly be probabilities? Justifyyour answer a 0.462 b −0.201 c 1 d 5/6 e 3.5 f 0
4.3 Playing Cards An ordinary deck of playing cards has 52 cards There are
four suits—spades, hearts, diamonds, and clubs—with 13 cards in each suit.Spades and clubs are black; hearts and diamonds are red If one of these cards isselected at random, what is the probability that it is a spade? b red? c not aclub?
4.4 Poker Chips A bowl contains 12 poker chips—3 red, 4 white, and 5 blue If
one of these poker chips is selected at random from the bowl, what is theprobability that its color is a red? b red or white? c not white?
4.5 Prospects for Democracy In the journal article “The 2003–2004 Russian
Elections and Prospects for Democracy” (Europe-Asia Studies, Vol 57, No 3, pp.369–398), R Sakwa examined the fourth electoral cycle that independent Russiaen- tered in 2003 The following frequency table lists the candi- dates andnumbers of votes from the presidential election on March 14, 2004
Candidate VotesPutin, Vladimir 49,565,23
8 Kharitonov,
Nikolai
9,513,313 Glaz’ev, Sergei 2,850,063 Khakamada, Irina 2,671,313 Malyshkin, Oleg 1,405,315 Mironov, Sergei 524,324Find the probability that a randomly selected voter voted for a Putin b eitherMalyshkin or Mironov c someone other than Putin
Trang 74.6 Cardiovascular Hospitalizations From the Florida State Center for HealthStatistics report Women and Cardiovascular Disease Hospitalization, we obtainedthe following table show- ing the number of female hospitalizations forcardiovascular disease, by age group, during one year.
Age group (yr) Number0–19 810 20–39 5,029 40–49 10,977 50–59 20,983 60–69 36,884 70–79 65,017
80 andover 69,167One of these case records is selected at random Find the proba- bility that thewoman was a in her 50s b less than 50 years old c between 40 and 69 yearsold, inclusive d 70 years old or older
4.7 Housing Units The U.S Census Bureau publishes data on housing units inAmerican Housing Survey for the United States The following table provides afrequency distribution for the number of rooms in U.S housing units Thefrequencies are in thousands
Rooms No of units
4.8 Explain what is wrong with the following argument: When two balanced diceare rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11possibilities Therefore the probability is 1 11 that the sum is 12
4.9 Bilingual and Trilingual At a certain university in the United States, 62% ofthe students are at least bilingual— speaking English and at least one otherlanguage Of these stu- dents, 80% speak Spanish and, of the 80% who speakSpanish, 10% also speak French Determine the probability that a ran- domlyselected student at this university a does not speak Spanish b speaks Spanishand French
4.10 What does it mean for two events to be mutually exclusive? for threeevents?
4.11 Answer true or false to each statement, and give reasons for your answers
a If event A and event B are mutually exclusive, so are events A, B, andC for
Trang 8every event C b If event A and event B are not mutually exclusive, neither areevents A, B, andC for every event C.
4.12 Jurors From 10 men and 8 women in a pool of potential jurors, 12 arechosen at random to constitute a jury Suppose that you observe the number ofmen who are chosen for the jury Let A be the event that at least half of the 12jurors are men, and let B be the event that at least half of the 8 women are onthe jury a Determine the sample space for this experiment b Find (A or B), (A &B), and (A & (not B)), listing all the outcomes for each of those three events c.Are events A and B mutually exclusive? Are events A and (not B)? Are events (notA) and (not B)? Explain
4.13 Day Laborers Mary Sheridan, a reporter for The Wash- ington Post, wroteabout a study describing the characteristics of day laborers in the Washington,D.C., area (June 23, 2005, pp A1, A12) The study, funded by the Ford andRockefeller Foundations, interviewed 476 day laborers—who are becomingcommon in the Washington, D.C., area due to increase in con- struction andimmigration—in 2004 The following table provides a percentage distribution forthe number of years the day laborers lived in the United States at the time of theinterview
Years in U.S Percent
ageLess than 1 171–2 303–5 216–10 1211–20 13
21 or more 7Suppose that one of these day laborers is randomly selected a Without usingthe general addition rule, determine the probability that the day laborer obtainedhas lived in the United States either between 1 and 20 years, inclusive, or lessthan 11 years b Obtain the probability in part (a) by using the general additionrule c Which method did you find easier?
4.14 Coin Tossing A balanced dime is tossed twice The four possible equally
likely outcomes are HH, HT, TH, TT Let A = event the first toss is heads, B =event the second toss is heads, and C = event at least one toss is heads.Determine the following probabilities and express your results in words Computethe conditional probabilities directly; do not use the conditional probability rule
a P(B) b P(B|A) c P(B|C) d P(C) e P(C|A) f P(C|(not B)
4.15 Playing Cards One card is selected at random from an ordinary deck of 52
playing cards Let A = event a face card is selected, B = event a king is selected,and C = event a heart is selected Find the following probabilities and expressyour results in words Compute the conditional probabilities directly; do not usethe conditional probability rule a P(B) b P(B|A) c P(B|C) d P(B|(not A)) e P(A) f.P(A|B) g P(A|C) h P(A|(not B)
4.16 Suppose that A and B are two events a What does it mean for event B to
be independent of event A? b If event A and event B are independent, how cantheir joint probability be obtained from their marginal probabilities?
Trang 94.17 Cards Cards numbered 1,2,3, ,10 are placed in a box The box is shaken,
and a blindfolded person selects two suc- cessive cards without replacement a.What is the probability that the first card selected is num- bered 6? b Given thatthe first card is numbered 6, what is the probability that the second is numbered9? c Find the probability of selecting first a 6 and then a 9 d What is theprobability that both cards selected are numbered over 5?
4.18 Belief in Extraterrestrial Aliens According to an Opinion Dynamics Poll
published in USA TODAY, roughly 54% of U.S men and 33% of U.S womenbelieve in extraterrestrial aliens Of U.S adults, roughly 48% are men and 52%women a What percentage of U.S adults believe in such aliens? b Whatpercentage of U.S women believe in such aliens? c What percentage of U.S.adults that believe in such aliens are women?
4.19 Regarding permutations and combinations, a what is a permutation? b.what is a combination? c what is the major distinction between the two?
4.20 Computerized Testing A statistics professor needs to construct a question quiz, one question for each of five topics The computerized testingsystem she uses provides eight choices for the question on the first topic, ninechoices for the question on the second topic, seven choices for the question onthe third topic, eight choices for the question on the fourth topic, and six choicesfor the question on the fifth topic How many possibilities are there for the five-question quiz?
five-4.21 Telephone Numbers In the United States, telephone numbers consist of athree-digit area code followed by a seven- digit local number Suppose neitherthe first digit of an area code nor the first digit of a local number can be a zerobut that all other choices are acceptable a How many different area codes arepossible? b For a given area code, how many local telephone numbers arepossible? c How many telephone numbers are possible?
4.22 Determine the value of each quantity a 4P3 b 15P4 c 6P2 d 10P0 e 8P8
4.23 Determine the value of each quantity a 7P3 b 5P2 c 8P4 d 6P0 e 9P9
4.24 Determine the value of each of the following quantities a 4C3 b 15C4 c.6C2 d 10C0 e 8C8
4.25 A Lottery At a lottery, 100 tickets were sold and three prizes are to be
given How many possible outcomes are there if a the three prizes areequivalent? b there is a first, second, and third prize?
4.26 Shake Ten people attend a party If each pair of people shakes hands, how
many handshakes will occur?
Chương 5
Mục tiêu
1 use and understand the formulas in this chapter
2 determine the probability distribution of a discrete random variable
3 construct a probability histogram
4 describe events using random-variable notation, when appro- priate
Trang 105 use the frequentist interpretation of probability to under- stand the meaning ofthe probability distribution of a random variable.
6 find and interpret the mean and standard deviation of a dis- crete randomvariable
7 compute factorials and binomial coefficients
8 define and apply the concept of Bernoulli trials
9 assign probabilities to the outcomes in a sequence of Ber- noulli trials
10 obtain binomial probabilities
11 compute the mean and standard deviation of a binomial ran- dom variable
12 obtain Poisson probabilities
13 compute the mean and standard deviation of a Poisson ran- dom variable
14 use the Poisson distribution to approximate binomial proba- bilities, whenappropriate
Bài tập
5.8 Persons per Housing Unit From the document American Housing Survey forthe United States, published by the U.S Cen- sus Bureau, we obtained thefollowing frequency distribution for the number of persons per occupied housingunit, where we have used “7” in place of “7 or more.” Frequencies are in millions
of housing units
Persons 1 2 3 4 5 6 7
Frequen
cy 27.9 34.4 17.0 15.5 6.8 2.3 1.4For a randomly selected housing unit, let Y denote the number of persons living
in that unit a Identify the possible values of the random variable Y b Userandom-variable notation to represent the event that a housing unit has exactlythree persons living in it c Determine P(Y = 3); interpret in terms ofpercentages d Determine the probability distribution of Y e Construct aprobability histogram for Y
5.9 Color TVs The Television Bureau of Advertising, Inc., publishes information
on color television ownership in Trends in Television Following is a probabilitydistribution for the number of color TVs, Y, owned by a randomly selectedhousehold with annual income between $15,000 and $29,999
P(Y=y) 0.009 0.376 0.371 0.167 0.061 0.016
Use random-variable notation to represent each of the following events Thehouseholds owns a at least one color TV b exactly two color TVs c betweenone and three, inclusive, color TVs d an odd number of color TVs Use thespecial addition rule and the probability distribution to determine e P(Y ≥ 1) f.P(Y = 2) g P(1≤ Y ≤ 3) h P(Y = 1 or 3 or 5)
5.33 Equipment Breakdowns A factory manager collected data on the number
of equipment breakdowns per day From those data, she derived the probability
Trang 11distribution shown in the following table, where W denotes the number ofbreakdowns on a given day.
w 0 1 2P(W=w) 0.80 0.15 0.05
a Determine μW and σW b On average, how many breakdowns occur per day?
c About how many breakdowns are expected during a 1-year period, assuming
250 work days per year?
Chương 6
Mục tiêu
1 use and understand the formulas in this chapter
2 explain what it means for a variable to be normally dis- tributed orapproximately normally distributed
3 explain the meaning of the parameters for a normal curve
4 identify the basic properties of and sketch a normal curve
5 identify the standard normal distribution and the standard normal curve
6 use Table II to determine areas under the standard normal curve
7 use Table II to determine the z-score(s) corresponding to a specified areaunder the standard normal curve
8 use and understand the zα notation
9 determine a percentage or probability for a normally dis- tributed variable
10 state and apply the 68.26-95.44-99.74 rule
11 determine the observations corresponding to a specified per- centage orprobability for a normally distributed variable
12 explain how to assess the normality of a variable with a nor- mal probabilityplot
13 construct a normal probability plot with the aid of Table III
14 use a normal probability plot to detect outliers
15.* approximate binomial probabilities by normal-curve areas, whenappropriate
Bài tập
6.48 According to Table II, the area under the standard normal curve that lies tothe left of−2.08 is 0.0188 Without further con- sulting Table II, determine thearea under the standard normal curve that lies to the right of 2.08 Explain yourreasoning
6.49 According to Table II, the area under the standard normal curve that lies tothe left of 0.43 is 0.6664 Without further con- sulting Table II, determine the areaunder the standard normal curve that lies to the right of 0.43 Explain yourreasoning
Trang 126.50 According to Table II, the area under the standard normal curve that lies tothe left of 1.96 is 0.975 Without further consult- ing Table II, determine the areaunder the standard normal curve that lies to the left of−1.96 Explain yourreasoning.
6.55 Determine the area under the standard normal curve that lies to the left of
a 2.24 b −1.56 c 0 d −4
6.56 Determine the area under the standard normal curve that lies to the left of
a −0.87 b 3.56 c 5.12 6.57 Find the area under the standard normal curvethat lies to the right of a −1.07 b 0.6 c 0 d 4.2
6.59 Determine the area under the standard normal curve that lies between a
−2.18 and 1.44 b −2 and−1.5 c 0.59 and 1.51 d 1.1 and 4.2
6.60 Determine the area under the standard normal curve that lies between a
−0.88 and 2.24 b −2.5 and−2 c 1.48 and 2.72 d −5.1 and 1
6.67 Obtain the z-score for which the area under the standard normal curve to itsleft is 0.025
6.68 Determine the z-score for which the area under the standard normal curve
to its left is 0.01
6.69 Find the z-score that has an area of 0.75 to its left under the standardnormal curve
6.75 Find the following z-scores a z0.03 b z0.005
6.76 Obtain the following z-scores a z0.20 b z0.06
6.79 Complete the following table
z0.10 z0.05 z0.025 z0.01 z0.005
1.28
6.86 A variable is normally distributed with mean 68 and stan- dard deviation 10.Find the percentage of all possible values of the variable that a lie between 73and 80 b are at least 75 c are at most 90
6.87 A variable is normally distributed with mean 10 and stan- dard deviation 3.Find the percentage of all possible values of the variable that a lie between 6and 7 b are at least 10 c are at most 17.5
6.94 Serum Cholesterol Levels According to the National Health and Nutrition
Examination Survey, published by the National Center for Health Statistics, theserum (noncellular portion of blood) total cholesterol level of U.S females 20years old or older is normally distributed with a mean of 206 mg/dL (milligramsper deciliter) and a standard deviation of 44.7 mg/dL a Determine thepercentage of U.S females 20 years old or older who have a serum totalcholesterol level between 150 mg/dL and 250 mg/dL b Determine thepercentage of U.S females 20 years old or older who have a serum totalcholesterol level below 220 mg/dL c Obtain and interpret the quartiles for serumtotal cholesterol level of U.S females 20 years old or older d Find and interpretthe fourth decile for serum total cholesterol level of U.S females 20 years old orolder
Trang 136.107 For a normally distributed variable, fill in the blanks a % of all possibleobservations lie within 1.96 standard deviations to either side of the mean b %
of all possible observations lie within 1.64 standard deviations to either side ofthe mean
6.108 For a normally distributed variable, fill in the blanks a 99% of all possibleobservations lie within standard de- viations to either side of the mean b 80% ofall possible observations lie within standard de- viations to either side of themean
6.111 Let x be a normally distributed variable with mean μ and standarddeviation σ a Express the quartiles, Q1, Q2, and Q3, in terms of μ and σ b.Express the k th percentile, Pk, in terms of μ, σ, andk
Chương 7
Mục tiêu
1 use and understand the formulas in this chapter
2 define sampling error, and explain the need for sampling distributions 3 findthe mean and standard deviation of the variable ¯ x, given the mean andstandard deviation of the population and the sample size
4 state and apply the central limit theorem
5 determine the sampling distribution of the sample mean when the variableunder consideration is normally distributed
6 determine the sampling distribution of the sample mean when the sample size
of the population mean, μ d 100(1−α)% of all possible samples have meansthat lie within of the population mean, μ.(Hint: Draw a graph for the distribution
of ¯ x, and determine the z-scores dividing the area under the normal curve into
a middle 1−α area and two outside areas of α/2.)
7.82 Testing for Content Accuracy A brand of water-softener salt comes in
packages marked “net weight 40 lb.” The company that packages the salt claimsthat the bags contain an average of 40 lb of salt and that the standard deviation
of the weights is 1.5 lb Assume that the weights are normally distributed a.Obtain the probability that the weight of one randomly selected bag of water-
Trang 14softener salt will be 39 lb or less, if the company’s claim is true b Determine theprobability that the mean weight of 10 randomly selected bags of water-softenersalt will be 39 lb or less, if the company’s claim is true c If you bought one bag
of water-softener salt and it weighed 39 lb, would you consider this evidence thatthe company’s claim is incorrect? Explain your answer d If you bought 10 bags
of water-softener salt and their mean weight was 39 lb, would you consider thisevidence that the company’s claim is incorrect? Explain your answer
Chương 8
Mục tiêu
1 use and understand the formulas in this chapter
2 obtain a point estimate for a population mean
3 find and interpret a confidence interval for a population mean when thepopulation standard deviation is known
4 compute and interpret the margin of error for the estimate of μ
5 understand the relationship between sample size, standard deviation,confidence level, and margin of error for a con- fidence interval for μ
6 determine the sample size required for a specified confidence level andmargin of error for the estimate of μ
7 understand the difference between the standardized and studentized versions
8.7 Fuel Tank Capacity Consumer Reports provides informa- tion on new
automobile models—including price, mileage rat- ings, engine size, body size,and indicators of features A simple random sample of 35 new models yieldedthe following data on fuel tank capacity, in gallons
Trang 15automobile models Assume σ = 3.50 gallons.c How would you decide whetherfuel tank capacities for new automobile models are approximately normallydistributed? d Must fuel tank capacities for new automobile models be exactlynormally distributed for the confidence interval that you obtained in part (b) to
be approximately correct? Explain your answer
8.10 Serum Cholesterol Levels Information on serum total cholesterol level is
published by the Centers for Disease Control and Prevention in National Healthand Nutrition Examination Survey A simple random sample of 12 U.S females 20years old or older provided the following data on serum total cholesterol level, inmilligrams per deciliter (mg/dL)
260 289 190 214 110 241 169 173 191 178 129 185
a Obtain a normal probability plot of the data b Based on your result frompart (a), is it reasonable to pre- sume that serum total cholesterol level ofU.S females 20 years old or older is normally distributed? Explain youranswer c Find and interpret a 95.44% confidence interval for the meanserum total cholesterol level of U.S females 20 years old or older Thepopulation standard deviation is 44.7 mg/dL d In Exercise 6.94, we notedthat the mean serum total choles- terol level of U.S females 20 years old
or older is 206 mg/dL Does your confidence interval in part (c) contain thepopulation mean? Would it necessarily have to? Explain your answers
8.31 Venture-Capital Investments Data on investments in the high-tech
industry by venture capitalists are compiled by VentureOne Corporation andpublished in America’s Network Telecom Investor Supplement A random sample
of 18 venture- capital investments in the fiber optics business sector yielded thefollowing data, in millions of dollars
5.6
0 6.27 5.96 10.51 2.04 5.48 5.74 5.58 4.13 8.63 5.95 6.67 4.21 7.71 9.21 4.98 8.64 6.66
a Determine a 95% confidence interval for the mean amount, μ, of all capital investments in the fiber optics busi- ness sector Assume that thepopulation standard deviation is $2.04 million (Note: The sum of the data is
venture-$113.97 million.) b Interpret your answer from part (a)
8.44 Family Size The U.S Census Bureau compiles data on family size and
presents its findings in Current Population Re- ports Suppose that 500 U.S.families are randomly selected to es- timate the mean size, μ, of all U.S families.Further suppose that the results are as shown in the following frequencydistribution
8.52 In each part, explain the effect on the margin of error and hence the effect
on the precision of estimating a population mean by a sample mean a