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

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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
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
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
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
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
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
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.
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)
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
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
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)
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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.
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
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
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
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 .
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( )

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.

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.

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.

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.

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.

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

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.

=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.

= 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%?

=(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.

=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?

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.

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