商务统计学笔试复习题

一、The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.1., the population of interest isa)all the customers who have bought a videocassette recorder made by thecompany over the past 12 months.b)all the customers who have bought a videocassette recorder made by thecompany and brought it in for repair over the past 12 months.c)all the customers who have used a videocassette recorder over the past 12months.d)all the customers who have ever bought a videocassette recorder made by thecompany.ANSWER:a2., which of the following will be a good frame for drawing a sample?a)Telephone directory.b)Voting registry.c)The list of customers who returned the registration card.d) A list of potential customers purchased from a database marketing company.ANSWER:c3.the possible responses to the question "How many videocassette recorders made byother manufacturers have you used?" are values from aa)discrete random variable.b)continuous random variable.c)categorical random variable.d)parameter.ANSWER:a4.the possible responses to the question "Are you happy, indifferent, or unhappy withthe performance per dollar spent on the videocassette recorder?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: categorical random variable, types of data5.the possible responses to the question "What is your annual income rounded to thenearest thousands?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:a6.the possible responses to the question "How much time do you use the videocassetterecorder every week on the average?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:b7.the possible responses to the question "How many people are there in yourhousehold?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:a8.the possible responses to the question "How would you rate the quality of yourpurchase experience with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?"are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER: c9.the possible responses to the question "What brand of videocassette recorder did youpurchase?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:c10.the possible responses to the question "Out of a 100 point score with 100 being thehighest and 0 being the lowest, what is your satisfaction level on the videocassetterecorder that you purchased?" are values from aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:a11.the possible responses to the question "In which year were you born?" are valuesfrom aa)discrete numerical random variable.b)continuous numerical random variable.c)categorical random variable.d)parameter.ANSWER:a二、The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The total number of students in the sample who visited campus bars on the weekend before the final exam week is an example ofe) a categorical random variable.f) a discrete random variable.g) a continuous random variable.h) a parameter.ANSWER:b三、T he chancellor of a major university was concerned about alcohol abuse on her campusand wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students and computed the portion of students in the sample who visited campus bars on the weekend before the final exam. The portion of all students at her university who visited campus bars on the weekend before the final exam week is an example ofi) a categorical random variable.j) a discrete random variable.k) a continuous random variable.l) a parameter.ANSWER:d四、T he chancellor of a major university was concerned about alcohol abuse on her campusand wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The portion of students in the sample who visited campus bars on the weekend before the final exam week is an example of __________.m)a categorical random variable.n) a discrete random variable.o) a parameter.p) a statisticANSWER:d五、The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.Defects1 2 4 4 5 5 6 7 9 9 12 12 1517 20 21 23 23 25 26 27 27 28 29 291.Referring to Table 2-11, if a frequency distribution for the defects data is constructed,using "0 but less than 5" as the first class, the frequency of the “20 but less than 25”class would be ________.ANSWER:42.Referring to Table 2-11, if a frequency distribution for the defects data is constructed,using "0 but less than 5" as the first class, the relative frequency of the “15 but lessthan 20” class would be ________.ANSWER:0.08 or 8% or 2/253.Referring to Table 2-11, construct a frequency distribution for the defects data, using"0 but less than 5" as the first class.ANSWER:Defects Frequency0 but less than 5 45 but less than 10 610 but less than 15 215 but less than 20 220 but less than 25 425 but less than 30 74.Referring to Table 2-11, construct a relative frequency or percentage distribution forthe defects data, using "0 but less than 5" as the first class.ANSWER:Defects Percentage0 but less than 5 165 but less than 10 2410 but less than 15 815 but less than 20 820 but less than 25 1625 but less than 30 285.Referring to Table 2-11, construct a cumulative percentage distribution for the defectsdata if the corresponding frequency distribution uses "0 but less than 5" as the first class.ANSWER:Defects C umPct0 05 1610 4015 4820 5625 7230 1006.Referring to Table 2-11, construct a histogram for the defects data, using "0 but lessthan 5" as the first class.ANSWER:7. Referring to Table 2-11, construct a cumulative percentage polygon for the defectsdata if the corresponding frequency distribution uses "0 but less than 5" as the first class.ANSWER:Cumulative Percentage Polygon0%10%20%30%40%50%60%70%80%90%100%0510********Number of Defects六、Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows:60 61 62 63 64 65 66 68 68 69 70 73 7374 75 76 76 81 81 82 86 87 89 90 921. Referring to Table 3-1, calculate the arithmetic mean age of the uninsured seniorcitizens to the nearest hundredth of a year.ANSWER:74.04 years2. Referring to Table 3-1, identify the median age of the uninsured senior citizens.ANSWER:73 years3. Referring to Table 3-1, identify the first quartile of the ages of the uninsured seniorcitizens.ANSWER:65.5 years4.Referring to Table 3-1, identify the third quartile of the ages of the uninsured seniorcitizens.ANSWER:81.5 years5.Referring to Table 3-1, identify the interquartile range of the ages of the uninsuredsenior citizens.ANSWER:16 years6.Referring to Table 3-1, identify which of the following is the correct statement.a)One fourth of the senior citizens sampled are below 65.5 years of age.b)The middle 50% of the senior citizens sampled are between 65.5 and 73.0years of age.c)The average age of senior citizens sampled is 73.5 years of age.d)All of the above are correct.ANSWER:a7.Referring to Table 3-1, identify which of the following is the correct statement.a)One fourth of the senior citizens sampled are below 64 years of age.b)The middle 50% of the senior citizens sampled are between 65.5 and 73.0years of age.c)25% of the senior citizens sampled are older than 81.5 years of age.d)All of the above are correct.ANSWER:c8.Referring to Table 3-1, what type of shape does the distribution of the sample appearto have?ANSWER:Slightly positive or right-skewed.9.Referring to Table 3-1, calculate the variance of the ages of the uninsured seniorcitizens correct to the nearest hundredth of a year squared.ANSWER:94.96 years210.Referring to Table 3-1, calculate the standard deviation of the ages of the uninsuredsenior citizens correct to the nearest hundredth of a year.ANSWER:9.74 years11.Referring to Table 3-1, calculate the coefficient of variation of the ages of theuninsured senior citizens.ANSWER:13.16%七、The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days.STEM LEAVES1H 678892L 334442H 55666788993L 1122Note (1): 1H means the “high teens” 15, 16, 17, 18, or 19; 2L means the “lowtwenties” 20, 21, 22, 23, or 24; 2H means the “high twenties” 25, 26, 27, 28, or 29, etc.Note (2): For this sample, the sum of the observations is 838, the sum of the squares of the observations is 20,684, and the sum of the squared differences between eachobservation and the mean is 619.89.1.Referring to Table 3-4, the arithmetic mean of the customs data is ________.ANSWER:23.92.Referring to Table 3-4, the median of the customs data is ________.ANSWER:233.Referring to Table 3-4, the first quartile of the customs data is ________.ANSWER:214.Referring to Table 3-4, the third quartile of the customs data is ________.ANSWER:275.Referring to Table 3-4, the range of the customs data is ________.ANSWER:166.Referring to Table 3-4, the interquartile range of the customs data is ________.ANSWER:67.Referring to Table 3-4, the variance of the customs data is ________.ANSWER:18.28.Referring to Table 3-4, the standard deviation of the customs data is ________.ANSWER:4.39.Referring to Table 3-4, the coefficient of variation of the customs data is ________percent.ANSWER:17.8% or 18%10.Referring to Table 3-4, the five-number summary for the data in the customs sampleconsists of ________, ________, ________, ________, ________.ANSWER:16, 21, 23, 27, 3211.Referring to Table 3-4, construct a boxplot of this sample.Box-and-whisker Plot101520253035ANSWER:八、Times spent studying by students in the week before final exams follow a normaldistribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.1.what is the probability that the sample mean exceeds the population mean by morethan 2 hours?ANSWER:0.30852.what is the probability that the sample mean is more than 3 hours below thepopulation mean?ANSWER:0.22663.what is the probability that the sample mean differs from the population mean by lessthan 2 hours?ANSWER:0.3829 using Excel or 0.3830 using Table E.24.what is the probability that the sample mean differs from the population mean bymore than 3 hours?ANSWER:0.4533 using Excel or 0.4532 using Table E.2九、A quality control engineer is interested in the mean length of sheet insulation being cutautomatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.1.Referring to Table 8-3, the critical value to use in obtaining the confidence interval is________.ANSWER:2.582.Referring to Table 8-3, the confidence interval goes from ________ to ________.ANSWER:12.09 to 12.193.True or False: Referring to Table 8-3, the confidence interval indicates that themachine is not working properly.ANSWER:True4.True or False: Referring to Table 8-3, the confidence interval is valid only if thelengths cut are normally distributed.ANSWER:FalseEXPLANATION: With a sample size of 70, this confidence interval will still be valid if the lengths cut are not normally distributed due to the central limit theorem.KEYWORDS: confidence interval, mean, standardized normal distribution, central limit theorem5.Referring to Table 8-3, suppose the engineer had decided to estimate the mean lengthto within 0.03 with 99% confidence. Then the sample size would be ________.ANSWER:165.8724 rounds up to 166十、A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?a)Z-test of a population meanb)Z-test of a population proportionc)t-test of population meand)t-test of a population proportionANSWER:c十一、A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a samplestandard deviation of $23.65. If you wanted to test whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?e)There is not evidence that the average balance is $75.f)There is not evidence that the average balance is not $75.g)There is evidence that the average balance is $75.h)There is evidence that the average balance is not $75.ANSWER:d十二、The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?i)Z-test of a population meanj)Z-test of a population proportionk)t-test of population meanl)t-test of a population proportionANSWER:b十三、A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.2.Referring to Table 9-2, what would be a Type I error?a)Saying that the person is a business major when in fact the person is abusiness major.b)Saying that the person is a business major when in fact the person is anagriculture major.c)Saying that the person is an agriculture major when in fact the person is abusiness major.d)Saying that the person is an agriculture major when in fact the person is anagriculture major.ANSWER:c3.Referring to Table 9-2, what would be a Type II error?a)Saying that the person is a business major when in fact the person is abusiness major.b)Saying that the person is a business major when in fact the person is anagriculture major.c)Saying that the person is an agriculture major when in fact the person is abusiness major.d)Saying that the person is an agriculture major when in fact the person is anagriculture major.ANSWER:b4.Referring to Table 9-2, what is the “actual level of significance” of the test?a)0.13b)0.16c)0.84d)0.87ANSWER:a5.Referring to Table 9-2, what is the “actual confidence coefficient”?a)0.13b)0.16c)0.84d)0.87ANSWER:d6.Referring to Table 9-2, what is the value of ?a)0.13b)0.16c)0.84d)0.87ANSWER:a7.Referring to Table 9-2, what is the value of ?a)0.13b)0.16c)0.84d)0.87ANSWER:b十四、Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.American JapaneseSample Size 211 100Mean SSATL Score 65.75 79.83Population Std. Dev. 11.07 6.411.Referring to Table 10-1, judging from the way the data were collected, which testwould likely be most appropriate to employ?a)Paired t testb)Pooled-variance t test for the difference between two meansc)Independent samples Z test for the difference between two meansd)Related samples Z test for the mean differenceANSWER:c2.Referring to Table 10-1, give the null and alternative hypotheses to determine if theaverage SSATL score of Japanese managers differs from the average SSATL score of American managers.a)H0: μA–μJ≥0 ver sus H1: μA–μJ<0b)H0:μA–μJ≤0 ver sus H1: μA–μJ>0c)H0: μA–μJ=0 ver sus H1:μA–μJ≠0d)H0:X A–X J=0 versus H1:X A–X J≠0ANSWER:c3.Referring to Table 10-1, assuming the independent samples procedure was used,calculate the value of the test statistic.a)Z=65.75–79.83 9.82211+9.82100b) Z =65.75–79.8311.07211+6.41100c) Z =65.75–79.839.822211+9.822100d) Z =65.75–79.8311.072211+6.412100ANSWER:d4. Referring to Table 10-1, suppose that the test statistic is Z = 2.45. Find the p -value ifwe assume that the alternative hypothesis was a two-tailed test (0– :1≠J A H μμ).a) 0.0071 b) 0.0142 c) 0.4929 d)0.9858ANSWER: b十五、An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:ANOVASource of Variation SS df MSF P-value F crit Between Groups 212.4 3 8.3049850.0014743.238867Within Groups 136.48.525Total348.81. Referring to Table 10-15, the within groups degrees of freedom ise) 3 f) 4 g) 16h)19ANSWER:c2.Referring to Table 10-15, the total degrees of freedom isi) 3j) 4k)16l)19ANSWER:d3.Referring to Table 10-15, the among-group (between-group) mean squares ism)8.525n)70.8o)212.4p)637.2ANSWER:b4.Referring to Table 10-15, at a significance level of 1%,q)there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.r)there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.s)there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.t)there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.ANSWER:c十六、A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in SanDiego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status(Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident.The number of children in each category is given in the table below.1.Referring to Table 11-1, the calculated test statistic isa)-0.9991b)-0.1368c)48.1849d)72.8063ANSWER:c2.Referring to Table 11-1, at 5% level of significance, the critical value of the teststatistic isa) 3.8415b) 5.9914c)9.4877d)13.2767ANSWER:a3.Referring to Table 11-1, at 5% level of significance, there is sufficient evidence toconclude thata)use of seat belts in motor vehicles is related to ethnic status in San DiegoCounty.b)use of seat belts in motor vehicles depends on ethnic status in San DiegoCounty.c)use of seat belts in motor vehicles is associated with ethnic status in SanDiego County.d)All of the above.ANSWER:d十七、A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a compa ny is the company’s sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:E(Y)=β0+β1XThe results of the simple linear regression are provided below.µ2,70020, 65, two-tailed value 0.034 (for testing )YX Y X S p β1=-+==1. Referring to Table 12-1, interpret the estimate of β0, the Y -intercept of the line. a) All companies will be charged at least $2,700 by the bank.b) There is no practical interpretation since a sales revenue of $0 is anonsensical value.c) About 95% of the observed service charges fall within $2,700 of the leastsquares line.d) For every $1 million increase in sales revenue, we expect a service charge todecrease $2,700.ANSWER: b2. Referring to Table 12-1, interpret the estimate of , the standard deviation of therandom error term (standard error of the estimate) in the model.a) About 95% of the observed service charges fall within $65 of the leastsquares line.b) About 95% of the observed service charges equal their correspondingpredicted values.c) About 95% of the observed service charges fall within $130 of the leastsquares line.d) For every $1 million increase in sales revenue, we expect a service charge toincrease $65.ANSWER: c3. Referring to Table 12-1, interpret the p -value for testing whether β1 exceeds 0.a) There is sufficient evidence (at the = 0.05) to conclude that sales revenue (X )is a useful linear predictor of service charge (Y ).b) There is insufficient evidence (at the = 0.10) to conclude that sales revenue(X ) is a useful linear predictor of service charge (Y ).c) Sales revenue (X ) is a poor predictor of service charge (Y ).d) For every $1 million increase in sales revenue, we expect a service charge toincrease $0.034.ANSWER: a4. Referring to Table 12-1, a 95% confidence interval for β1 is (15, 30). Interpret theinterval.a)We are 95% confident that the mean service charge will fall between $15 and$30 per month.b)We are 95% confident that the sales revenue (X) will increase between $15and $30 million for every $1 increase in service charge (Y).c)We are 95% confident that average service charge (Y) will increase between$15 and $30 for every $1 million increase in sales revenue (X).d)At the = 0.05 level, there is no evidence of a linear relationship betweenservice charge (Y) and sales revenue (X).ANSWER:c。