商务统计学第八章习题

1、精选优质文档-倾情为你奉上精选优质文档-倾情为你奉上专心-专注-专业专心-专注-专业精选优质文档-倾情为你奉上专心-专注-专业CHAPTER 8: CONFIDENCE INTERVAL ESTIMATIONThe width of a confidence interval estimate for a proportion will benarrower for 99% confidence than for 95% confidence.wider for a sample size of 100 than for a sample size of 50.narrower for 90%

2、 confidence than for 95% confidence.narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.ANSWER:cTYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, properties, widthWhen determining the sample size for a proportion for a given level of confidence

3、and sampling error, the closer to 0.50 that is estimated to be, the sample size required _.is smalleris largeris not affectedcan be smaller, larger or unaffectedANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, propertiesA 99% confidence interval estimate can be interp

4、reted to mean thatif all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.we have 99% confidence that we have selected a sample whose interval does include the population mean.Both of the ab

5、ove.None of the above.ANSWER:cTYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, interpretationIf you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, the critical value of t will be2.79692.787

6、42.49222.4851ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: critical value, t distributionWhich of the following is not true about the Students t distribution?It has more area in the tails and less in the center than does the normal distribution.It is used to construct confidence intervals for the popu

7、lation mean when the population standard deviation is known.It is bell shaped and symmetrical.As the number of degrees of freedom increases, the t distribution approaches the normal distribution.ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, propertiesTrue or False: The t distribution i

8、s used to construct confidence intervals for the population mean when the population standard deviation is unknown.ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standard deviation unknownThe t distribution assumes the population is normally distributed.approaches the norm

9、al distribution as the sample size increases.has more area in the tails than does the normal distribution.All of the above.ANSWER:dTYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, propertiesIt is desired to estimate the average total compensation of CEOs in the Service industry. Data were randoml

10、y collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.We are 97% confident that the mean of the sampled CEOs falls i

11、n the interval $2,181,260 to $5,836,180.In the population of Service industry CEOs, 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,2

12、60 to $5,836,180.ANSWER:dTYPE: MC DIFFICULTY: DifficultKEYWORDS: confidence interval, interpretationIt is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5

13、,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?Yes, and I am 97% confident of it.Yes, and I am 78% confident of it.I am 97% confident that the average compensation is $3,000,000.I cannot conclude that the

14、average exceeds $3,000,000 at the 97% confidence level.ANSWER:dTYPE: MC DIFFICULTY: DifficultKEYWORDS: confidence interval, interpretationA confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the followi

15、ng 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?No, and we are 90% sure of it.No. The proportion is 54.17%.Maybe. 0.60 is a believable value of the population proportion based on the information above.Yes, and we are 90%

16、sure of it.ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, proportion, testingA confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642

17、). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?105150420597ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: proportion, sample size determinationWhen determining the sample size necessary for es

18、timating the true population mean, which factor is not considered when sampling with replacement? The population size.The population standard deviation.The level of confidence desired in the estimate.The allowable or tolerable sampling error.ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: mean, sample si

19、ze determinationSuppose a 95% confidence interval for turns out to be (1,000, 2,100). Give a definition of what it means to be “95% confident” as an inference.In repeated sampling, the population parameter would fall in the given interval 95% of the time.In repeated sampling, 95% of the intervals co

20、nstructed would contain the population mean.95% of the observations in the entire population fall in the given interval.95% of the observations in the sample fall in the given interval.ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, interpretationSuppose a 95% confidence interval

21、 for turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?Increase the sample size.Increase the confidence level.Increase the population mean.Increase

22、 the sample mean.ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, properties, widthSuppose a 95% confidence interval for has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would . (

23、Assume that the sample statistics gathered would not change very much for the new sample.)be larger than the current interval widthbe narrower than the current interval widthbe the same as the current interval widthbe unknown until actual sample sizes and reliability levels were determinedANSWER:bTY

24、PE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, properties, widthIn the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a interval.narrowerwiderless significantbiasedANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: confiden

25、ce interval, properties, widthA major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chains new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: and . Assu

26、ming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for ?Approximately normal with a mean of $50.50A standard normal distributionA t distr

27、ibution with 15 degrees of freedomA t distribution with 14 degrees of freedomANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: confidence interval, mean, t distributionA major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the c

28、hains new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: and . Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chains new store in the mall assuming that the amount

29、spent follows a normal distribution.$50.50 $9.09$50.50 $10.12$50.50 $11.00$50.50 $11.08ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: confidence interval, mean, t distributionPrivate colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of

30、 this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value

31、will be used as the point estimate for the mean endowment of all private colleges in the United States?$1,447.8$180.975$143.042$8ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: point estimate, meanPrivate colleges and universities rely on money contributed by individuals and corporations for their operat

32、ing expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, a

33、nd 220.0. Summary statistics yield and . Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.$180.975$94.066$180.975$99.123$180.975$116.621$180.975$119.586ANSWER:dTYPE: MC DIFFICULTY: ModerateKE

34、YWORDS: confidence interval, mean, t distributionA university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $55 per credit hour. The university system administrators are contemplating charging each

35、student a set fee of $750 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of

36、 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How la

37、rge a total sample would they need to take?ANSWER:n = 2033TYPE: PR DIFFICULTY: EasyKEYWORDS: mean, sample size determinationAs an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during

38、a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, and s2 = 25. Which of the following assumptions is necessary in order for a confidence interval to be valid?The population sampled from has an approximate n

39、ormal distribution.The population sampled from has an approximate t distribution.The mean of the sample equals the mean of the population.None of these assumptions are necessary.ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, mean, t distributionAs an aid to the establishment of

40、personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, and s2 = 25. E

41、stimate the mean number of admissions per 24-hour period with a 95% confidence interval.ANSWER:19.8 1.249TYPE: PR DIFFICULTY: ModerateKEYWORDS: confidence interval, mean, t distributionAs an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean nu

42、mber of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, and s2 = 25. Using the sample standard deviation as an estimate for the population standard dev

43、iation, what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability,?ANSWER:n = 166TYPE: PR DIFFICULTY: ModerateKEYWORDS: mean, sample size determinationA university dean is interested in determinin

44、g the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive

45、financial aid.ANSWER:0.59 0.057 or 0.533 0.647TYPE: PR DIFFICULTY: ModerateKEYWORDS: confidence interval, proportionA university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly se

46、lects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 0.59 0.07. Interpret this interval.We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.95% of the students get between 52% and 66

47、% of their tuition paid for by financial aid.We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.We are 95% confident that 59% of the students are on some sort of financial aid.ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: confidence interval, pr

48、oportion, interpretationA university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wante

49、d to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?n = 1,844n = 1,784n = 1,503n = 1,435ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: proportion, sample size determinationAn economist is interested in st

50、udying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?$15,052$15,141$15,330$15,364ANS

51、WER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: confidence interval, mean, standardized normal distributionAn economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average

52、 income of $15,000. What is the width of the 90% confidence interval?$232.60$364.30$465.23$728.60ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: width, confidence interval, mean, standardized normal distributionAn economist is interested in studying the incomes of consumers in a particular region. Th

53、e population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?n = 1537n = 385n = 40n = 2

54、0ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: mean, sample size determinationThe head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books pe

55、r day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress?7408309201,660ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: point estimate, meanThe head librarian at the Library of Congress has asked her assistant for an interval estimate of t

56、he mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, approximately how large a sample did her assistant use to determin

57、e the interval estimate?2312It cannot be determined from the information given.ANSWER:dTYPE: MC DIFFICULTY: DifficultKEYWORDS: mean, sample size determinationThe head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each da

58、y. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant

59、 use to determine the interval estimate?12513114ANSWER:cTYPE: MC DIFFICULTY: DifficultKEYWORDS: mean, sample size determinationThe head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the f

60、ollowing interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval