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Chapter 08 Sampling Distributions and Estimation Answer Key     Multiple Choice Questions   48. A sampling distribution describes the distribution of:    A.  a parameter. B.  a statistic. C.  either a parameter or a statistic. D.  neither a parameter nor a statistic. A statistic has a sampling distribution.   AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 08-03 State the Central Limit Theorem for a mean. Topic: Sample Mean and the Central Limit Theorem   49. As the sample size increases, the standard error of the mean:    A.  increases. B.  decreases. C.  may increase or decrease. The standard error of the mean is σ/(n) 1/2 .   AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 08-03 State the Central Limit Theorem for a mean.
Topic: Sample Mean and the Central Limit Theorem   50. Which statement is most nearly correct, other things being equal?    A.  Doubling the sample size will cut the standard error of the mean in half. B.  The standard error of the mean depends on the population size. C.  Quadrupling the sample size roughly halves the standard error of the mean. D.  The standard error of the mean depends on the confidence level. The standard error of the mean is σ/(n) 1/2 so replacing n by 4n would cut the SEM in half.   AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 08-04 Explain how sample size affects the standard error. Topic: Sample Mean and the Central Limit Theorem   51. The width of a confidence interval for μ is not affected by:    A.  the sample size. B.  the confidence level. C.  the standard deviation. D.  the sample mean. The mean is not used in calculating the width of the confidence interval zσ/(n) 1/2 .   AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 08-05 Construct a 90; 95; or 99 percent confidence interval for μ. Topic: Confidence Interval for a Mean (μ) with Known σ   52. The Central Limit Theorem (CLT) implies that:    A.  the population will be approximately normal if n ≥ 30.
B.  repeated samples must be taken to obtain normality. C.  the distribution of the mean is approximately normal for large n. D.  the mean follows the same distribution as the population. The sampling distribution of the mean is asymptotically normal for any population.   AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 08-03 State the Central Limit Theorem for a mean. Topic: Sample Mean and the Central Limit Theorem   53. The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent CI for the true mean client age is approximately:    A.  ± 1.711 years. B.  ± 2.326 years. C.  ± 2.492 years. D.  ± 2.797 years. The width is ts/(n) 1/2 = (2.492)(5)/(25) 1/2 = 2.492.   AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 08-06 Know when to use Student's t instead of z to estimate μ. Topic: Confidence Interval for a Mean (μ) with Unknown σ   54. In constructing a confidence interval for a mean with unknown variance with a sample of 25 items, Bob used z instead of t. "Well, at least my interval will be wider than necessary, so it was a conservative error," said he. Is Bob's statement correct? 
  A.  Yes. B.  No. C.  It depends on μ. z is always smaller than t (ceteris paribus) so the interval would be narrower than is justified.   AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 08-06 Know when to use Student's t instead of z to estimate μ. Topic: Confidence Interval for a Mean (μ) with Unknown σ   55. A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is:    A.  ± 0.639 B.  ± 0.588 C.  ± 0.300 D.  ± 2.131 The width is ts/(n) 1/2 = (2.131)(1.2)/(16) 1/2 = 0.639.   AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 08-06 Know when to use Student's t instead of z to estimate μ. Topic: Confidence Interval for a Mean (μ) with Unknown σ   56. We could narrow a 95 percent confidence interval by: