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Department
Management
Course
MGMT 1050
Professor
All Professors
Semester
Winter

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Confidence Interval Estimation195 CHAPTER 8: CONFIDENCE INTERVAL ESTIMATION 1. The width of a confidence interval estimate for a proportion will be a) narrower for 99% confidence than for 95% confidence. b) wider for a sample size of 100 than for a sample size of 50. c) narrower for 90% confidence than for 95% confidence. d) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, properties, width 2. When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the __________ the sample size required. a) smaller b) larger c) The sample size is not affected. d) The effect cannot be determined from the information given. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, properties 3. A 99% confidence interval estimate can be interpreted to mean that a) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. b) we have 99% confidence that we have selected a sample whose interval does include the population mean. c) both of the above d) none of the above ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, interpretation 4. If 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 be a) 2.7970. b) 2.7874. c) 2.4922. d) 2.4851. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: critical value, t distribution 5. Which of the following is NOT true about the Student’s t distribution? 196 Confidence Interval Estimation a) It has more area in the tails and less in the center than does the normal distribution. b) It is used to construct confidence intervals for the population mean when the population standard deviation is known. c) It is bell shaped and symmetrical. d) As the number of degrees of freedom increases, the t distribution approaches the normal distribution. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, properties 6. True or False: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standard deviation unknown 7. The t distribution a) assumes the population is normally distributed. b) approaches the normal distribution as the sample size increases. c) has more area in the tails than does the normal distribution. d) all of the above ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, properties 8. It 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, $5,836,180). Which of the following interpretations is correct? a) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180. b) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180. c) 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. d) We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence interval, interpretation Confidence Interval Estimation197 9. It 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, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000? a) Yes, and I am 97% confident of it. b) Yes, and I am 78% confident of it. c) I am 97% confident that the average compensation is $3,000,000. d) I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence interval, interpretation 10. A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60? a) No, and we are 90% sure of it. b) No. The proportion is 54.17%. c) Maybe. 0.60 is a believable value of the population proportion based on the information above. d) Yes, and we are 90% sure of it. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, testing 11. A 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). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ± 0.08 using 95% confidence? a) 105 b) 150 c) 420 d) 597 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: proportion, sample size determination 198 Confidence Interval Estimation 12. When determining the sample size necessary for estimating the true population mean, which factor is NOT considered when sampling with replacement? a) the population size b) the population standard deviation c) the level of confidence desired in the estimate d) the allowable or tolerable sampling error ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, sample size determination μ 13. Suppose a 95% confidence interval for turns out to be (1,000, 2,100). Give a definition of what it means to be “95% confident” in an inference. a) In repeated sampling, the population parameter would fall in the given interval 95% of the time. b) In repeated sampling, 95% of the intervals constructed would contain the population mean. c) 95% of the observations in the entire population fall in the given interval. d) 95% of the observations in the sample fall in the given interval. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, interpretation 14. Suppose a 95% confidence interval 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? a) Increase the sample size. b) Decrease the confidence level. c) Increase the sample size and decrease the confidence level. d) Increase the confidence level and decrease the sample size. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, properties, width Confidence Interval Estimation 199 15. Suppose a 95% confidence interval forμ 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 . (Assume that the sample statistics gathered would not change very much for the new sample.) a) be larger than the current interval width b) be narrower than the current interval width c) be the same as the current interval width d) be unknown until actual sample sizes and reliability levels were determined ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, properties, width 16. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a interval. a) narrower b) wider c) less significant d) biased ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, properties, width 17. A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fif2een credit card accounts were randomly sampled and analyzed with the following resultX = $50.50 and s = 400 . Assuming 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 ? a) approximately normal with a mean of $50.50 b) a standard normal distribution c) a t distribution with 15 degrees of freedom d) a t distribution with 14 degrees of freedom ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 200 Confidence Interval Estimation 18.A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: and 2 . X = $50.50 s = 400 Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain’s new store in the mall, assuming that the amount spent follows a normal distribution. a) $50.50 ± $9.09 b) $50.50 ± $10.12 c) $50.50 ± $11.00 d) $50.50 ± $11.08 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 19. Private colleges and universities rely on money contributed by individuals and corporations for their operating 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, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? a) $1,447.8 b) $180.975 c) $143.042 d) $8 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate, mean 20.Private colleges and universities rely on money contributed by individuals and corporations for their operating 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, and 220.0. Summary statistics yield and s =143.042 . X = 180.975 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. a) $180.975 ± $94.066 ± b) $180.975 $99.123 c) $180.975 ± $116.621 d) $180.975 ± $119.605 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution Confidence Interval Estimation 201 21. A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Presently the students pay $55 per credit hour. The university system administrators are contemplating charging each 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 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 large a sample would they need to take? ANSWER: n = 2033 TYPE: PR DIFFICULTY: Easy KEYWORDS: mean, sample size determination 22. As 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 a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of 2 admissions for each. For this sampleX = 19.8 and s = 25. Which of the following assumptions is necessary in order for a confidence interval to be valid? a) The population sampled from has an approximate normal distribution. b) The population sampled from has an approximate t distribution. c) The mean of the sample equals the mean of the population. d) None of these assumptions are necessary. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 23. As 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 a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sampleX = 19.8 and s = 25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval. ANSWER: 19.8 ± 1.249 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 202 Confidence Interval Estimation 24. As 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 a 24-hour period. The director randomly selects 64 different224-hour periods and determines the number of admissions for each. For this samplX = 19.8 and s = 25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose? ANSWER: n = 166 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean, sample size determination 25. A 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. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid. ANSWER: 0.59 0.057 ± TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 26. A 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. The 95% confidence interval for p is 0.59± 0.07. Interpret this interval. a) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. b) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. c) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. d) We are 95% confident that 59% of the students are on some sort of financial aid. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation Confidence Interval Estimation203 27. A 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 wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled? a) n = 1,844 b) n = 1,784 c) n = 1,503 d) n = 1,435 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: proportion, sample size determination 28. An 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 income of $15,000. What is the upper end point in a 99% confidence interval for the average income? a) $15,052 b) $15,141 c) $15,330 d) $15,364 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standardized normal distribution 29. An 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 income of $15,000. What is the width of the 90% confidence interval? a) $232.60 b) $364.30 c) $465.23 d) $728.60 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: width, confidence interval, mean, standardized normal distribution 204 Confidence Interval Estimation 30. An 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 income of $15,000. What 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? a) n = 1537 b) n = 385 c) n = 40 d) n = 20 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, sample size determination 31. The 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 per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress? a) 740 b) 830 c) 920 d) 1,660 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate, mean 32. The 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 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 determine the interval estimate? a) 2 b) 3 c) 12 d) It cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: mean, sample size determination Confidence Interval Estimation205 33. The 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 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 use to determine the interval estimate? a) 125 b) 13 c) 11 d) 4 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: mean, sample size determination 34. The 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 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 estimate? a) 99.7% b) 99.0% c) 98.0% d) 95.4% ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: mean, sample size determination 35. True or False: A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 4.52 seconds to 5.18 seconds. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 36. True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7, a 90% confidence interval will have a width of 2.36. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 206 Confidence Interval Estimation 37. True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7, a 90% confidence interval will have a width of 2.36. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution 38. True or False: A sample size of 5 provides a sample mean of 9.6. If the population variance is known to be 5 and the population distribution is assumed to be normal, the lower limit for a 92% confidence interval is 7.85. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution 39.True or False: A random sample of 50 provides a sample mean of 31 with a standard deviation of s=14. The upper bound of a 90% confidence interval estimate of the population mean is 34.32. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 40.True or False: In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedomfrom the t distribution equals 22. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 41. True or False: Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, properties 42.True or False: The t distribution allows the calculation of confidence intervals for means when the actual standard error is not known. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 43.True or False: The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population. Confidence Interval Estimatio207 ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 44. True or False: For a t distribution with 12 degrees of freedom, the area between – 2.6810 and 2.1788 is 0.980. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: t distribution 45. True or False: A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 0.95 confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 46. True or False: The sample mean is a point estimate of the population mean. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate, mean 47. True or False: The confidence interval estimate of the population mean is constructed around the sample mean. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean 48. True or False: The confidence interval estimate of the population proportion is constructed around the sample proportion. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 208 Confidence Interval Estimation 49. True or False: A point estimate consists of a single sample statistic that is used to estimate the true population parameter. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate 50. True or False: The confidence interval obtained will always correctly estimate the population parameter. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, interpretation 51. True or False: Other things being equal, the confidence interval for the mean will be wider for 95% confidence than for 90% confidence. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, properties, width 52.True or False: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 53.True or False: The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, t distribution 54. True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, standardized normal distribution Confidence Interval Estimatio209 55. True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, standardized normal distribution 56. True or False: The t distribution approaches the standardized normal distribution when the number of degrees of freedomincreases. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t distribution, standardized normal distribution 57. True or False: In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 58. True or False: The difference between the sample mean and the population mean is called the sampling error. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 59. True or False: The difference between the sample proportion and the population proportion is called the sampling error. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 60. True or False: The difference between the sample size and the population size is called the sampling error. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling error 210 Confidence Interval Estimation 61. True or False: The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 62. True or False: The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 63. True or False: Sampling error equals to half the width of a confidence interval. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 64. True or False: The width of a confidence interval equals twice the sampling error. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 65. True or False: The sampling error can either be positive or negative. ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling error 66. True or False: A population parameter is used to estimate a confidence interval. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate, confidence interval Confidence Interval Estimation211 67. True or False: For a given data set and confidence level, the confid
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