Statistics for Business and Economics 8th Edition by Paul Newbold William Carlson Betty Thorne Test Bank

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Statistics for Business and Economics 8th Edition by Paul Newbold William Carlson Betty Thorne Test Bank

Description

CHAPTER 7
Estimation: Single Population

Multiple-Choice Questions

1. In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past month. Which of the following intervals represents a 98% confidence interval for the population proportion?

A) 0.137 to 0.192
B) 0.140 to 0.189
C) 0.129 to 0.199
D) 0.143 to 0.186
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider the following point estimators, W, X, Y, and Z of : ; ; ; and .

2. Which of the following point estimators is the most efficient?

A) W
B) X
C) Y
D) Z
ANSWER: A
Difficulty: 2 Moderate
Topic: Properties of Point Estimators
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

3. What is the relative efficiency of W with respect to X?

A) 0.9
B) 1.6
C) 1.1
D) 0.4
ANSWER: C
Difficulty: 2 Moderate
Topic: Properties of Point Estimators
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

4. What is the relative efficiency of Z with respect to Y?

A) 0.50
B) 0.80
C) 1.20
D) 1.50
ANSWER: C
Difficulty: 2 Moderate
Topic: Properties of Point Estimators
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

5. The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet.,. Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail?

A) 912 49.2
B) 912 42.6
C) 912 44.3
D) 912 46.8
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

6. The number of television sets produced from an assembly line each day is known to have a standard deviation of 17.4 sets per day. The production line averaged 452.3 sets per day for 20 randomly selected days. Which of the following represents a 95% confidence interval for the population mean number of sets per hour?

A) 452.3 9.4
B) 452.3 11.3
C) 452.3 13.8
D) 452.3 7.63
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

7. Which of the following statements is true regarding the width of a confidence interval for a population proportion?

A) It is narrower for 95% confidence than for 90% confidence.
B) It is wider for a sample of size 80 than for a sample of size 40.
C) It is wider for 95% confidence than for 99% confidence.
D) It is narrower when the sample proportion is 0.20 than when the sample proportion is 0.50.
ANSWER: D
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

8. Let , , , and be a random sample of observations from a population with mean and variance . Consider the following estimator of : = 0.15 + 0.35 + 0.20 + 0.30 . What is the variance of ?

A)
B)
C) 0.55
D)
ANSWER: B
Difficulty: 1 Easy
Topic: Properties of Point Estimators
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

9. In a survey of 472 personnel directors, 63% thought that they would be hiring new personnel over the next three months. Which of the following represents a 98% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?

A) 0.63 0.057
B) 0.63 0.047
C) 0.63 0.042
D) 0.63 0.052
ANSWER: D
Difficulty: 2 Moderate
Topic:
Confidence Interval Estimation for Population Proportion (Large Samples)

AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

10. The manager of the local health club is interested in determining the number of times members use the weight room per month. She takes a random sample of 15 members and finds that over the course of a month, the average number of visits was 11.2 with a standard deviation of 3.2. Assuming that the monthly number of visits is normally distributed, which of the following represents a 95% confidence interval for the average monthly usage of all health club members?

A) 11.2 1.74
B) 11.2 1.77
C) 11.2 1.62
D) 11.2 1.83
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

11. For a population that is normally distributed with a very large population size compared to the sample size, the variance of the sample mean is given by ____.

A)
B)
C)
D)
ANSWER: D
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

THE NEXT FOUR QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6. For a random sample of 12 hours, the average number of beverage cans produced was 326.0. Assume a 99% confidence interval for the population mean number of beverage cans produced per hour.

12. Calculate the margin of error of the 99% confidence interval.

A) 1.85
B) 3.60
C) 6.41
D) 10.56
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

13. Calculate the width of the 99% confidence interval estimate.

A) 12.81
B) 3.21
C) 6.41
D) 7.20
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

14. Find the upper confidence limit of the 99% confidence interval.

A) 340.25
B) 325.98
C) 319.59
D) 332.41
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

15. Find the lower confidence limit of the 99% confidence interval.

A) 340.25
B) 325.98
C) 319.59
D) 332.41
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known

AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

16. The dollar value of orders placed through a particular store catalog is found to be normally distributed with a standard deviation of $21.58. A sample of 30 orders averaged $81.25. What is the 90% confidence interval around this sample mean?

A) $81.25 $21.58
B) $81.25 $10.79
C) $81.25 $12.15
D) $81.25 $6.48
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known

AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

THE NEXT SIX QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes. A random sample of 75 patients in the local hospital had a mean time of 90 minutes. Assume a 95% confidence interval for the population mean .

17. What is the formula used to calculate the standard error?

A)
B)
C)
D)
ANSWER: A
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

18. Calculate the standard error of the 95% confidence interval.

A) 0.40
B) 3.46
C) 13.69
D) 2.50
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

19. Calculate the margin of error of the 95% confidence interval.

A) 5.69
B) 8.93
C) 6.79
D) 8.06
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

20. Calculate the width of the 95% confidence interval estimate.

A) 16.12
B) 11.38
C) 17.86
D) 13.58
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

21. Find the upper confidence limit of the 95% confidence interval.

A) 95.68
B) 98.07
C) 96.79
D) 94.43
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

22. Find the lower confidence limit of the 95% confidence interval.

A) 83.21
B) 85.57
C) 81.93
D) 84.32
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

THE NEXT FIVE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes) it takes to commute to school for six days. Those results are: 25, 22, 17, 20, 15, and 10. Assuming the population is normally distributed, develop a 90% confidence interval for the population mean.

23. What is the value of the sample mean?

A) 22.6
B) 20.4
C) 16.8
D) 18.2
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

24. What is the value of the ample standard deviation?

A) 4.88
B) 4.25
C) 5.34
D) 3.64
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

25. Determine the reliability factor from the Students t distribution table.

A) 1.476
B) 2.015
C) 3.365
D) 4.032
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

26. Find the upper confidence limit of the 90% confidence interval.

A) 13.81
B) 18.24
C) 21.59
D) 25.89
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

27. Find the lower confidence limit of the 90% confidence interval.

A) 13.81
B) 18.24
C) 22.59
D) 25.89
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

28. In developing an interval estimate for a population mean, the population standard deviation is assumed to be 8. The interval estimate is 45.82 2.36. What will be the interval estimate for the population mean if is equal to 16?

A) 45.82 4.72
B) 45.82 2.36
C) 45.82 9.44
D) 45.82 5.56
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

29. In developing an interval estimate for a population mean, a sample of 40 observations was used. The interval estimate was 28.76 1.48. Had the sample size been 160 instead of 40, the interval estimate would have been ____.

A) 28.76 0.37
B) 28.76 0.74
C) 28.76 1.48
D) 28.76 2.96
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

30. A 95% confidence interval estimate for a population mean is determined to be 65.48 to 76.52. Which of the following is true if a 90% confidence interval for is constructed?

A) It is wider than the 95% confidence interval
B) It is the same as the 95% confidence interval
C) It is narrower than the 95% confidence interval
D) There is not enough information to determine the answer.
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

31. Interval estimates for the variance of a normal population rely on the random variable , which follows ____.

A) a normal distribution
B) a binomial distribution
C) the Poisson distribution
D) a chi-square distribution
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

32. If a sample of size 200 has 40 successes, the lower limit of a confidence interval at the 95% level of confidence for the population proportion is ____.

A) 0.2554
B) 0.1446
C) 0.2465
D) 0.1535
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

33. The 95% confidence interval for the population proportion P, given a sample size n = 2200 and sample proportion = 0.214 is computed as ____.

A) 0.214 0.017
B) 0.214 0.048
C) 0.214 0.069
D) 0.214 0.086
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

34. The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion = 0.62 is equal to ____.

A) 0.715
B) 0.699
C) 0.525
D) 0.440
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

35. The upper limit of 90% confidence interval for the population proportion P, given a sample size n = 300 and sample proportion = 0.1833 is equal to ____.

A) 0.1466
B) 0.1395
C) 0.2271
D) 0.2200
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

36. Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?

A) the t-distribution with n+1 degrees of freedom
B) the t-distribution with n degrees of freedom
C) the t-distribution with n-1 degrees of freedom
D) the t-distribution with 2n degrees of freedom
ANSWER: C
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

37. The 95% confidence interval for the population proportion P given a sample size n = 300 and sample proportion = 0.2933 is calculated as ____.

A) 0.2933 0.0515
B) 0.2933 0.0289
C) 0.2933 0.9200
D) 0.2933 0.8145
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

38. Which of the following statements is true?

A) If a sample has 16 observations and a 90% confidence estimate for is needed, the appropriate t-score is 1.753.
B) If a sample has 16 observations and a 99% confidence estimate for is needed, the appropriate t-score is 2.602.
C) If a sample has 20 observations and a 95% confidence estimate for is needed, the appropriate t-score is 1.729.
D) If a sample has 20 observations and a 98% confidence estimate for is needed, the appropriate t-score is 2.093.
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

39. If a sample has 20 observations and a 90% confidence estimate for is needed, the appropriate t-score is ____.

A) 2.120
B) 1.746
C) 2.131
D) 1.729
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

40. If a sample of size 30 is selected, the value of A for the probability P(t A) = 0.01 is ____.

A) 2.247
B) 2.045
C) 2.462
D) 2.750
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown

AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

41. If a sample of size 21 is selected, the value of A for the probability P(t A) = 0.025 is ____.

A) 2.528
B) 2.086
C) 2.518
D) 2.080
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

42. The following sample was taken from a normally distributed population: 20, 27, 15, 20, 16, 22, and 13. A 95% confidence interval for the population mean using this sample is ____.

A) 19 5.603
B) 19 2.201
C) 19 8.804
D) 19 4.402
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

43. If a sample of size 61 is selected, the value of A for the probability P(-A t A) = 0.95 is ____.

A) 2.000
B) 2.021
C) 1.677
D) 1.671
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

44. If a sample of size 41 is selected, the value of A for the probability P(-A t A) = 0.90 is ____.

A) 1.303
B) 1.684
C) 2.021
D) 2.423
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

45. In order to estimate the average daily down time, a manufacturer randomly sampled 41days of production records and found a mean of 51.75 minutes and standard deviation of 7.9 minutes. A 90% confidence interval for the population mean is ____.

A) 51.75 4.76
B) 51.75 3.28
C) 51.75 2.08
D) 51.75 1.30
ANSWER: C
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

46. If a sample of size 120 is selected, the value of A for the probability P(-A t A) = 0.98 is:

A) 1.960.
B) 2.576.
C) 1.282.
D) 2.326.
ANSWER: D
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

47. A sample of 50 students is taken from Utah Valley University (UVU). These students spent an average of $175 on books this semester, with a standard deviation of $25. A 95% confidence interval for the average amount of money spent on books for all students at UVU is equal to____. (Hint: Use Excel function to obtain the critical value.)

A) 175 3.47
B) 175 7.18
C) 175 7.51
D) 175 3.86
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

48. A random sample of size 15 is taken from a normally distributed population with a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean is equal to ____.

A) 77.530
B) 72.231
C) 74.727
D) 79.273
ANSWER: A
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

49. Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence interval for the population variance?

A) 11.39 to 15.86
B) 3.11 to 29.51
C) 6.54 to 38.82
D) 1.12 to 5.69
ANSWER: B
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let , , , and be a random sample of observations from a population with mean and variance . Consider the following two point estimators of :
= 0.10 + 0.40 + 0.40 + 0.10 and
= 0.20 + 0.30 + 0.30 + 0.20

50. Which of the following statements is true?

A) is biased, but is an unbiased estimator of .
B) is unbiased, but is a biased estimator of .
C) Both and are unbiased estimators of .
D) Both and are biased estimators of .
ANSWER: C
Difficulty: 2 Moderate
Topic: Properties of Point Estimators
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

51. Which of the following constraints is true?

A) Var( ) = Var( )
B) Var( ) > Var( )
C) Var( ) < Var( ) D) ANSWER: B Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 52. What is the relative efficiency of with respect to ? A) 1.05 B) 0.98 C) 1.30 D) 0.76 ANSWER: D Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation True-False Questions 53. The point estimator is said to be an unbiased estimator of if Var( ) = Var( ). ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 54. The bias of an estimator is equal to E( ) . ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Analytic Course LO: Discuss the Applications of Confidence Interval Estimation 55. If the population is normally distributed, both the sample mean and the median are unbiased estimators of the population mean. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 56. If Var = 2 and Var = 22, then the relative efficiency of with respect to is equal to 0.5. ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 57. All other things being equal, the larger the sample size, the narrower the interval estimates that reflect the uncertainty about a parameters true value. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 58. A sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate is an unbiased estimator. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 59. The lower limit of the 90% confidence interval for the population proportion P, given that n = 400; and = 0.10 is 0.1247. ANSWER: F Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 60. When computing the confidence interval for the population proportion, the Students t-distribution is used rather than the normal distribution. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 61. The quantity 100(1+)% is called the confidence level of the interval. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 62. The width of a confidence interval is equal to twice the margin of error. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 63. For a 90% confidence interval, the reliability factor is equal to 1.96. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 64. If the shopping times for a random sample of 25 shoppers in a supermarket are normally distributed with a known population standard deviation of 15 minutes, the standard error is equal to 0.6. ANSWER: F Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 65. Keeping all other factors constant, the more the population standard deviation is reduced, the smaller the margin of error. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 66. The margin of error can be reduced by decreasing the sample size. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 67. Like the standard normal distribution, all t - distributions have a mean of zero and a standard deviation of 1. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 68. The larger the sampling error, the smaller the sample size needed to develop the confidence interval. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 69. The Students t distribution is the ratio of the standard normal distribution to the square root of the chi-square distribution divided by its degrees of freedom. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 70. The probability density functions of normal distributions and t distributions are symmetric about their means. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 71. As the confidence level for a confidence interval increases, the width of the interval also increases. ANSWER: T Difficulty: 1 Easy Topic: Sample-size Determination: Large Populations AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 72. An unbiased estimator of a population parameter is an estimator whose variance is the same as the actual value of the population variance. ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 73. The process of inferring the values of unknown population parameters from those of known sample statistics is called estimation. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 74. The density function of the standard normal distribution has a wider dispersion than the Students t distribution. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 75. Confidence intervals for the population proportion are centered on the sample proportion. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 76. A point estimate is an estimate of a population parameter expressed as a single numerical value. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 77. The t - distribution with n -1 degrees of freedom is often used to construct confidence intervals of the population mean when the population standard deviation is known. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 78. The sample standard deviation s is an unbiased estimator of the population standard deviation . ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 79. An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 80. An interval estimate is an interval that provides an upper and lower bound for a specific population parameter whose value is unknown. ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 81. An unbiased estimation procedure for the population total N yields the point estimate . ANSWER: T Difficulty: 1 Easy Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 82. The sample proportion is a biased estimator of the population proportion P. ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 83. Whatever the value of the sample proportion, cannot be smaller than 0.25. ANSWER: F Difficulty: 1 Easy Topic: Confidence Interval Estimation: Finite Populations AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 84. The maximum distance between an estimator and the true value of a parameter is called the margin of error. ANSWER: T Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 85. The value of the standard error of the mean is determined by dividing the total error by the sample size. ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 86. The bias of an unbiased estimator is equal to 1. ANSWER: F Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 87. If the campaign manager of a US senator is interested in estimating the proportion of registered voters who will support the senator during the next election, the sample proportion would be the appropriate point estimate. ANSWER: T Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 88. A point estimator is said to be more efficient than a point estimator if Var( ) > Var( ).

ANSWER: F
Difficulty: 1 Easy
Topic: Properties of Point Estimators
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

89. The normal distribution is used to develop a confidence interval estimate of the population proportion if the sample size is large.

ANSWER: T
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Analytic
Course LO: Discuss the Applications of Confidence Interval Estimation

90. The concept of margin of error is not applicable when estimating the population proportion P.

ANSWER: F
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

91. A 95% confidence interval estimate for a population mean is determined to be 62.8 to 73.4. If the confidence level is reduced to 90%, the confidence interval for becomes narrower.

ANSWER: T
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

92. A narrower confidence interval for a population parameter with a given confidence level can be obtained by increasing the sample size.

ANSWER: T
Difficulty: 1 Easy
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

93. A 95% confidence interval for the population proportion will not extend approximately 1.96 on each side of the sample proportion.

ANSWER: F
Difficulty: 2 Moderate
Topic: Sample-Size Determination: Finite Populations
AACSB: Reflective Thinking Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

Short Answer and Applied Questions

94. The number of bolts produced each hour from a particular machine is normally distributed with a standard deviation of 7.4. For a random sample of 15 hours, the average number of bolts produced was 587.3. Find the upper and lower confidence limits of a 98% confidence interval for the population mean number of bolts produced per hour.

ANSWER:
=7.4, = 587.3, n =15
. Hence, UCL = 591.75 and LCL = 582.85
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known
AACSB:
Course LO: Discuss the Applications of Confidence Interval Estimation

95. In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past month. Develop a 95% confidence interval for the population proportion.

ANSWER:
= 0.164 1.96(0.0151) = 0.164 0.0296. Hence, UCL = 0.1936 and LCL = 0.1344.
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking
Course LO: Discuss the Applications of Confidence Interval Estimation

96. In a recent survey of 574 employees, 15.5% indicated that they were not in favor of a particular plan. What is the level of confidence is associated with the interval of 12.85% to 19.89%?

ANSWER:
=(0.1989-0.1285)/2 = 0.0352
. Hence = 0.01, or = 0.02. Then the confidence level is 98%.
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for Population Proportion (Large Samples)
AACSB: Reflective Thinking
Course LO: Discuss the Applications of Confidence Interval Estimation

97. A student records the time (in minutes) it takes to commute to school for seven days. Those results are: 21, 15, 13, 16, 10, 13, and 18. Assuming the population is normally distributed, develop a 95% confidence interval for the population mean.

ANSWER:
=15.143, s=3.625, = 2.447
.Hence, UCL=18.496 and LCL=11.79
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown
AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

98. You are told that a 95% confidence interval for the population mean is 17.3 to 24.5. If the population standard deviation is 18.2, how large was the sample?

ANSWER:
Width = =24.5 17.3 =7.2. Then, 2(1.96)
Difficulty: 2 Moderate
Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills
Course LO: Discuss the Applications of Confidence Interval Estimation

99. The amount of material used in making a custom sail for a sailboat is normally distributed. For a random sample of 15 sails, you find that the mean amount of material is 912 square feet, with a standard deviation of 64 square feet. Develop a 99% confidence interval for the population mean amount of material used in a custom sail.

ANSWER:
= 912 (2.977)(16.52) = 912 49.2 or 862.8 < < 961.2 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 100. You are interested in determining the amount of time (in minutes) you spend each day on the Internet. For seven days, these values are: 51, 24, 16, 88, 63, 28, and 59. Assume that the amount of time you spend on the Internet each day is normally distributed, and develop a 90% confidence interval for the population average amount of time. ANSWER: n =7, =47, s =25.65, =1.943. , or 28.16 < < 65.84 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 101. A mother who is interested in the true proportion of R-rated movies shown on pay TV by a cable system randomly selects 98 listings and finds 14 of them are R-rated movies. In her report to the subcommittee she wants to be 98% confident that the true proportion will be in an interval which she states. She has asked you to assist her by preparing a 98% confidence interval based on the data she collected. What should she report? ANSWER: or Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A Monte Carlo study involves 10,000 random samples of size 20 from a normal population with mean and standard deviation For each sample, the mean and the median are calculated, with the following results: Estimator Mean Median Average 120.2 119.96 Variance 25.52 67.89 102. What does the study suggest about the bias of the estimators in this situation? ANSWER: The two estimatorsthe mean and the medianappear to be unbiased. The averages are all very close to 120. This result should hold because the simulation uses a symmetric ( normal) population. Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 103. Which of the two estimators appears most efficient? ANSWER: The mean has the smallest variance, and therefore will have the smallest standard error. The sample mean appears most efficient. This result follows a normal population. It may not hold for other populations. Difficulty: 1 Easy Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let , , , and be a random sample of observations from a population with mean and variance . Consider the following two point estimators of : = 0.10 + 0.20 + 0.40 + 0.30 , and = 0.25 + 0.25 + 0.30 + 0.20 104. Show that both the estimators are unbiased. ANSWER: E( ) = 0.10 E( ) + 0.20 E( ) + 0.40 E( ) + 0.30 E( ) = 0.10 + 0.20 + 0.40 + 0.30 = E( ) = 0.25 E( ) + 0.25 E( ) + 0.30 E( ) + 0.20 E( ) = 0.25 + 0.25 + 0.30 + 0.20 = Since are both unbiased estimators of . Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 105. Which estimator is more efficient, or ? Explain in detail. ANSWER: Var( ) = Var(0.10 )+ Var(0.20 ) + Var(0.40 ) + Var(0.30 ) = 0.01 + 0.04 + 0.16 + 0.09 = 0.30 Var( ) = Var(0.25 )+ Var(0.25 ) + Var(0.30 ) + Var(0.20 ) = 0.0625 + 0.625 + 0.09 + 0.04 = 0.255 Since Var( ) < Var( ), then is more efficient than . Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 106. Find the relative efficiency of with respect to . ANSWER: Relative efficiency = Var /Var = 0.30/0.255 = 1.176 Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 107. Raising in-state and out-of-state tuition is supposed to reduce the number of students in state supported universities. The registrar of a university wants to estimate the proportion P of students who are paying for out-of-state tuition on the installment plan (to later be compared with in-state installment plan payers). A random sample of 80 students who live out-of-state is taken and 50 of them pay tuition on the installment plan. Find a 99-percent confidence interval for P, based on these data. ANSWER: or Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The Daytona Beach Tourism Commission is interested in the average amount of money a typical college student spends per day during spring break. They survey 35 students and find that the mean spending is $63.57 with a standard deviation of $17.32. 108. Develop a 95% confidence interval for the population mean daily spending. ANSWER: = 63.57 2.042(17.32) / 5.9 = 63.57 = 63.57 5.978 Then, UCL = 69.548 and LCL = 57.592. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 109. Interpret the confidence level in the previous question. ANSWER: If independent random samples of size 35 are repeatedly selected from the population and 95% confidence intervals for each of these samples are determined, then over a very large number of repeated trials, 955 of these intervals will contain the value of the true average amount of money a typical college student spends per day during spring break. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Course LO: Discuss the Applications of Confidence Interval Estimation 110. What level of confidence is associated with an interval of $58.62 to $68.52 for the population mean daily spending? ANSWER: = (68.52 58.62) / 2 = 4.95 . Hence, = 0.05, or = 0.10. Then the confidence level is 90%. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A researcher is interested in determining the percentage of all households in the U.S. that have more than one home computer. In a survey of 492 households, 27% indicated that they own more than one home computer. 111. Develop a 90% confidence interval for the proportion of all households in the U.S. with more than one computer. ANSWER: n = 492, =0.27, =1.645 . Hence, UCL= 0.303 and LCL = 0.237 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 112. The researcher reports a confidence interval of 0.2312 to 0.3096 but neglects to tell you the confidence level. What is the confidence level associated with this interval? ANSWER: Width = 2 =0.3096-0.2312 = 0.0784 Then, = 0.0784 0.04 = 0.0784 =1.96. Hence, = 0.025, or = 0.05. Then, the confidence level is 95%. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A computer is programmed to draw 1000 samples, each of size 40 from a normally distributed population having mean 50 and standard deviation 10. For each sample, the mean and the median are computed. The average value and standard deviation of each set of estimates for the 1000 samples are as follows. Statistic Average Value Standard Deviation Mean 50.1278 2.2132 Median 50.2109 2.8263 113. Do the two statistics appear to be unbiased? ANSWER: The average value of each estimator is very close to the population mean 50, so both estimators appear to be unbiased. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 114. Which statistic appears to be more efficient? ANSWER: The sample mean has the smallest standard error, so it appears to be most efficient in this situation. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the amount of time teenagers spend on the internet is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. 115. Determine the 95% confidence interval estimate of the population mean. ANSWER: 6.206 < < 6.794 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 116. Interpret what the interval estimate in the previous question tells you. ANSWER: If we repeatedly draw independent random samples of size 100 from the population of teenagers and confidence intervals for each of these samples are determined, then over a very large number of repeated trials, 95% of these confidence intervals will contain the value of the true population mean amount of time teenagers spend on the internet. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT FOUR QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The data shown below specify how much a sample of 20 executives paid in federal income taxes, as a percentage of gross income, are reproduced below. 18.0 20.1 20.6 22.2 23.7 24.4 24.4 25.1 25.2 25.5 26.1 26.3 26.7 27.2 27.9 28.3 29.9 30.0 32.4 35.7 Assume that the standard deviation for the underlying population is equal to 4.0. 117. Calculate a 95% confidence interval for the population mean. ANSWER: The data above for a random sample of n = 20 yielded = 25.985 and we shall assume that = 4. Since implies the 95% confidence interval for is , or 24.232 < < 27.738. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 118. Calculate a 99% confidence interval for the population mean. ANSWER: Since then , or 23.681 < < 28.289. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 119. Give a careful verbal interpretation of the confidence interval in the previous question. ANSWER: We would expect that 99% of all confidence intervals calculated in this manner would include the true value of the parameter This means that if we sampled again and again (20 persons each time) and calculated a sample mean and a 99% confidence interval for the true mean each time, we would expect that 99% of them would include the population mean Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 120. Closed caption movies allow the hearing impaired to enjoy the dialogue as well as the acting. A local organization for the hearing impaired people of the community takes a random sample of 100 movie listings offered by the cable television company in order to estimate the proportion of closed caption movies offered. They observed that 14 movies were closed caption. The cable television company says at least 5% of the movies shown are closed captioned. Prepare a 90% confidence interval for the true proportion P and comment on the cable television company's claim. ANSWER: or The organization for hearing impaired people can be 90% confident that the proportion of closed caption movies offered is somewhere between 0.083 (8.3%) and 0.197 (19.7%). The cable television company could therefore conclude that at least 5% of the movies it shows are closed captioned. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The sales manager for a hardware wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements. Assume that the 500 calls represent a random sample. 121. Find a 95% confidence interval for the longrun proportion of new product placements. ANSWER: The sample proportion of calls that resulted in new product placement is implies A 95% confidence interval for P is or 0.414 < P < 0.502. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 122. Give a careful verbal interpretation of the confidence interval in the previous question. ANSWER: We are 95% confident that the true long run proportion of new product placements is in the interval (0.414, 0.502). By 95% confident we mean that if this experiment is conducted several times and a confidence interval is calculated for each trial, we expect 95% of them to include the true long run proportion. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 123. Find the confidence interval for estimating the population proportion for 90% confidence level; sample size n = 675; and sample proportion =0.10. ANSWER: , or 0.081 < P < 0.119 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Reflective Thinking Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWINGINFORMATION: A furniture mover calculates the actual weight as a proportion of estimated weight for a sample of 31 recent jobs. The sample mean is 1.13 and the sample standard deviation is 0.16. 124. Calculate a 95% confidence interval for the population mean using t tables. ANSWER: Given: n = 31, and s = 0.16. To calculate a 95% confidence interval, we need the t table value for v = 30. With this value is The confidence interval is or Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 125. Assume that the population standard deviation is known to be 0.16. Calculate a 95% confidence interval for the population mean using the z- table. ANSWER: If is known to be 0.16, we may use the z table value (rather than the t table value) in the 95% confidence interval. or Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 126. Are the intervals calculated in the previous two questions of roughly similar size? Explain. ANSWER: The two intervals are almost the same. The artificial (and probably incorrect) assumption that is equal to s allows us to quote a slightly narrower interval. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation ANSWER: THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regional CPA firm conducted an audit for a discount chain. One part of the audit involved developing an estimate for the mean dollar error in total charges that occur during the checkout process. They wish to develop a 90% confidence interval estimate for the population mean. A simple random sample of n = 20 is selected, with the following data (in dollars): 0.00 1.20 0.43 1.00 1.47 0.83 0.50 3.34 1.58 1.46 -0.36 -1.10 2.60 0.00 0.00 -1.70 0.83 1.99 0.00 1.34 127. Calculate the sample mean. ANSWER: Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 128. Calculate the sample standard deviation. ANSWER: Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 129. Develop a 90% confidence interval estimate for the population mean. ANSWER: , or $0.31< < $1.23 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 130. In a recent survey of personnel directors, 71% thought that they should hire new personnel over the next three months. The researcher conducting the survey reported that the 99% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months was from 0.68 to 0.74. What is the sample size taken by the researcher? ANSWER: Width = = 0.74-0.68 = 0.06 Then, 2(2.58) = 0.06 Difficulty: 2 Moderate Topic: Confidence Interval Estimation for Population Proportion (Large Samples) AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 131. The number of television sets coming off a production line each day is known to have a standard deviation of 118.5 sets per day. The production manager tells you that the 90% confidence interval for the population mean was 552.3 to 621.9. How large a sample was this confidence interval based on? ANSWER: Width = = 621.9-552.3 = 69.6 Then, 2(1.645) Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 132. The number of television sets coming off a production line each day is known to have a standard deviation of 17.4 sets per day. The production line averaged 852.3 sets per day for 20 randomly selected days. What is the level of confidence associated with the interval 844.75 to 860.0? ANSWER: Width = 2 =860-844.75-15.25. Then, . Hence, =1.96 and = 0.025. Therefore the confidence level is 95%. Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 133. There is concern about the speed of automobiles traveling over US 131. For a random sample of seven automobiles radar indicated the following speeds, in miles per hour: 80, 74, 69, 78, 87, 72, and 70. Assuming a normal population distribution, find the margin of error of a 95% confidence interval for the mean speed of all automobiles traveling over this stretch of highway. ANSWER: Margin of error: ME = = 2.447(6.3957/ ) = 5.9152 miles Difficulty: 2 Moderate Topic: Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT FOUR QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of ten homes in a particular suburb had the following selling prices (in thousands of dollars): 92, 83, 110, 115, 108, 96, 102, 90, 100, and 98. 134. Check for evidence of nonnormality. ANSWER: There is no evidence of nonnormality. Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Reflective Thinking Skills Course LO: Discuss the Applications of Confidence Interval Estimation 135. Find a point estimate of the population mean that is unbiased and efficient. ANSWER: The minimum variance unbiased point estimator of the population mean is the sample mean, where the value of the sample mean is 994 / 10 = 99.4 Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 136. Use an unbiased estimation procedure to find a point estimate of the variance of the sample mean. ANSWER: The unbiased point estimate of the variance of the sample mean: 862.4 / 9 = 95.822 Since = 95.822 / 10 = 9.582 Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation 137. Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $95,000. ANSWER: The sample proportion is an unbiased estimator of the population proportion P. Then, = 3 / 10 = 0.30 Difficulty: 2 Moderate Topic: Properties of Point Estimators AACSB: Analytic Skills Course LO: Discuss the Applications of Confidence Interval Estimation THE NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that and are random samples of observations from a population with mean and variance . Consider the following three point estimators, X, Y, and Z, of : , , and . 138. Show that all three estimators X, Y, and Z are unbiased. ANSWER: Since , all three estimators are unbiased. Difficulty: 3 Challenging Topic: Properties of Point Estimat

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