Ch.8 Statistical Inference Estimation For Full Test Bank nan - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: Ch08, Chapter 8: Statistical Inference: Estimation for Single Populations
True/False
1. When a statistic calculated from sample data is used to estimate a population parameter, it is called a point estimate.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
2. When a range of values is used to estimate a population parameter, it is called a range estimate.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
3. If the population is not normal but its standard deviation, σ is known and the sample size, n is large (n ≥ 30), z-distribution values may be used to determine interval estimates for the population mean.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
4. If the population is normal and its standard deviation, σ, is known but the sample size is small, z-distribution values may not be used to determine interval estimates for the population mean.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
5. If the population is normal and its standard deviation, σ, is known and the sample size, n, is large (n ≥ 30), interval estimates for the population mean must be determined using z-values.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
6. Suppose a random sample of 16 is selected from a population with a normal distribution with a known population standard deviation σ of 10. Assume that the sample mean is 4.2. Based on a 90% confidence interval for the population mean, we can conclude that 0.1 is a plausible number for the population mean μ.
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Hard
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
7. You are thinking of using a t-table to find a 95 percent confidence interval for the mean μ of a population. The distribution of the population is normal and the population standard deviation is unknown. A random sample of size n is drawn from this population. You may use the t-distribution only if the sample size n is small.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Hard
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
8. When the population standard deviation, σ, is unknown the sample standard deviation, s, is used in determining the interval estimate for the population mean.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
9. An assumption underlying the use of t-statistic in sample-based estimation is that the population is normally distributed.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
10. A t-distribution is similar to a normal distribution, but with flatter tails.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
11. In order to find values in the t distribution table, you must determine the appropriate degrees of freedom based on the sample sizes.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
12. If the degrees of freedom in a t distribution increase, the difference between the t values and the z values will also increase.
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
13. In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the z-distribution.
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
14. A market researcher computed a confidence interval for a population proportion using a 95% confidence level. Her boss decided that she wanted a 99% confidence level instead. The new interval with 99% confidence level will be wider than the original one with a 95% confidence level.
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
15. In determining the interval estimates for a population variance using the sample variance, it is appropriate to use the values from a chi-square distribution rather than a t-distribution.
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
16. Use of the chi-square statistic to estimate the population variance is extremely robust to the assumption that the population is normally distributed.
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
17. Like a t-distribution, a chi-square distribution is symmetrical and extends from minus infinity to plus infinity.
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
18. In estimating the sample size necessary to estimate a population mean, the error of estimation, E, is equal to the difference between the sample mean and the sample standard deviation.
Response: See section 8.5 Estimating Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
19. Given the error we are willing to tolerate, the sample size is determined by the mean, µ of the population and the confidence level.
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
Multiple Choice
20. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using _______.
a) a point estimate
b) a range estimate
c) a statistical parameter
d) an interval estimate
e) an exact estimate
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
21. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 45 randomly selected walk-in customers, and calculated that their mean waiting time was 15 minutes. If Brian concludes that the average waiting time for all walk-in customers is 15 minutes, he is using a ________.
a) a range estimate
b) a statistical parameter
c) an interval estimate
d) a point estimate
e) an exact estimate
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
22. Eugene Gates, Marketing Director of Mansfield Motors Manufacturers, Inc.’s Electrical Division, is leading a study to assess the relative importance of product features. An item on a survey questionnaire distributed to 100 of Mansfield’s customers asked them to rate the importance of “ease of maintenance” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). His staff assembled the following statistics.
Ease of Maintenance | |
Mean | 7.5 |
Standard Deviation | 1.5 |
If Eugene concludes that the average rate of “ease of maintenance” for all customers is 7.5, he is using ________.
a) a range estimate
b) a statistical parameter
c) a point estimate
d) an interval estimate
e) a guesstimate
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
23. The z value associated with a two‑sided 90% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
d) 2.575
e) 2.33
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
24. The z value associated with a two‑sided 95% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
d) 2.575
e) 2.33
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
25. The z value associated with a two‑sided 80% confidence interval is _______.
a) 1.645
b) 1.28
c) 0.84
d) 0.29
e) 2.00
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
26. The z value associated with a two‑sided 88% confidence interval is _______.
a) 1.28
b) 1.55
c) 1.17
d) 0.88
e) 1.90
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
27. Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a standard deviation of $0.23. Construct a 99% confidence interval to estimate the population mean.
a) $3.03 to $3.23
b) $3.12 to $3.14
c) $3.05 to $3.21
d) $2.90 to $3.36
e) $3.06 to $3.20
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
28. Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a standard deviation of $0.23. Construct a 92% confidence interval to estimate the population mean.
a) $3.03 to $3.23
b) $3.12 to $3.14
c) $3.05 to $3.21
d) $2.90 to $3.36
e) $3.06 to $3.20
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
29. Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a standard deviation of $0.23. Construct a 95% confidence interval to estimate the population mean.
a) $3.03 to $3.23
b) $3.12 to $3.14
c) $3.05 to $3.21
d) $2.90 to $3.36
e) $3.06 to $3.20
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
30. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is ________.
a) 14.27 to 15.73
b) 14.18 to 15.82
c) 9.88 to 20.12
d) 13.86 to 16.14
e) 18.12 to 19.87
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
31. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 95% confidence interval for the population mean of waiting times is ________.
a) 14.02 to 15.98
b) 7.16 to 22.84
c) 14.06 to 15.94
d) 8.42 to 21.58
e) 19.80 to 23.65
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
32. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff randomly selected personnel files for 100 tellers in the southeast region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 88% confidence interval for the population mean of training times is ________.
a) 17.25 to 32.75
b) 24.22 to 25.78
c) 24.42 to 25.59
d) 19.15 to 30.85
e) 21.00 t0 32.00
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
33. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff randomly selected personnel files for 100 tellers in the southeast region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 92% confidence interval for the population mean of training times is ________.
a) 16.25 to 33.75
b) 24.30 to 25.71
c) 17.95 to 32.05
d) 24.12 to 25.88
e) 24.45 to 27.32
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
34. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff randomly selected personnel files for 100 tellers in the southeast region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is ________.
a) 15.20 to 34.80
b) 24.18 to 25.82
c) 24.02 to 25.98
d) 16.78 to 33.23
e) 23.32 to 35.46
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
35. A random sample of 64 items is selected from a population of 400 items. The sample mean is 200. The population standard deviation is 48. From these data, the 95% confidence interval to estimate the population mean would be _______.
a) 189.21 to 210.79
b) 188.24 to 211.76
c) 190.13 to 209.87
d) 190.94 to 209.06
e) 193.45 to 211.09
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
36. A random sample of 64 items is selected from a population of 400 items. The sample mean is 200. The population standard deviation is 48. From these data, the 90% confidence interval to estimate the population mean would be _______.
a) 189.21 to 210.79
b) 188.24 to 211.76
c) 190.13 to 209.87
d) 190.94 to 209.06
e) 193.45 to 211.09
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
37. The z-distribution is used to estimate a population mean for large samples if the population standard deviation is known. "Large" is usually defined as _______.
a) at least 10
b) at least 5% of the population size
c) at least 30
d) at least 12
e) at least 100
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
38. If the standard deviation, σ is known the z-distribution values may not be used to determine interval estimates for the population mean when
a) n<30
b) the distribution is not normal
c) the distribution is skewed
d) n is big
e) n is small (<30) and the distribution is not normal
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population
39. The table t value associated with the upper 5% of the t distribution and 12 degrees of freedom is _______.
a) 2.179
b) 1.782
c) 1.356
d) 3.055
e) 3.330
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
40. The table t value associated with the upper 5% of the t distribution and 14 degrees of freedom is _______.
a) 2.977
b) 2.624
c) 2.145
d) 1.761
e) 1.345
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
41. The table t value associated with the upper 10% of the t distribution and 23 degrees of freedom is _______.
a) 1.319
b) 1.714
c) 2.069
d) 1.321
e) 2.332
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
42. A researcher is interested in estimating the mean weight of a semi tractor truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. She decides to construct a 98% confidence interval to estimate the mean. The degrees of freedom associated with this problem are _______.
a) 18
b) 17
c) 16
d) 15
e) 20
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
43. A researcher is interested in estimating the mean weight of a semi tractor truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi tractor truck is ______________.
a) 19,232 to 20,768
b) 19,365 to 20,635
c) 19,229 to 20,771
d) 19,367 to 20,633
e) 119.89 to 122.12
18,500 to 21,500
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
44. A researcher is interested in estimating the mean weight of a semi tractor truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 90% confidence interval for the population mean weight of a semi tractor truck is ______________.
a) 19,365 to 20,635
b) 19,367 to 20,633
c) 19,514 to 20,486
d) 19,515 to 20,485
e) 18,500 to 21,500
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
45. The weights of aluminum castings produced by a process are normally distributed. A random sample of 5 castings is selected; the sample mean weight is 2.21 pounds; and the sample standard deviation is 0.12 pound. The 98% confidence interval for the population mean casting weight is _________.
a) 1.76 to 2.66
b) 2.01 to 2.41
c) 2.08 to 2.34
d) 1.93 to 2.49
e) 2.49 to 2.67
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
46. Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________.
a) 63.37 to 86.63
b) 61.60 to 88.41
c) 71.77 to 78.23
d) 71.28 to 78.72
e) 79.86 to 81.28
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
47. Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 90% confidence interval for the population mean life of the new model is _________.
a) 66.78 to 83.23
b) 72.72 to 77.28
c) 72.53 to 77.47
d) 66.09 to 83.91
e) 73.34 to 76.25
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.
48. A researcher wants to estimate the proportion of the population which possesses a given characteristic. A random sample of size 800 is taken resulting in 360 items which possess the characteristic. The point estimate for this population proportion is _______.
a) 0.55
b) 0.45
c) 0.35
d) 0.65
e) 0.70
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Easy
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
49. A researcher wants to estimate the proportion of the population which possesses a given characteristic. A random sample of size 1800 is taken resulting in 450 items which possess the characteristic. The point estimate for this population proportion is _______.
a) 0.55
b) 0.45
c) 0.35
d) 0.25
e) 0.15
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Easy
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
50. A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own and iPhone. The 90% confidence interval to estimate the population proportion is ____.
a) 0.35 to 0.45
b) 0.34 to 0.46
c) 0.38 to 0.42
d) 0.39 to 0.41
e) 0.40 to 0.45
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
51. A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own and iPhone. The 95% confidence interval to estimate the population proportion is _______.
a) 0.35 to 0.45
b) 0.34 to 0.46
c) 0.37 to 0.43
d) 0.39 to 0.41
e) 0.40 to 0.42
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
52. A large trucking company wants to estimate the proportion of its tractor truck population with refrigerated carrier capacity. A random sample of 200 tractor trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is _______.
a) 0.53 to 0.67
b) 0.25 to 0.35
c) 0.24 to 0.36
d) 0.27 to 0.33
e) 0.28 to 0.34
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
53. A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 90% confidence interval to estimate the population proportion is _______.
a) 0.53 to 0.67
b) 0.25 to 0.35
c) 0.24 to 0.36
d) 0.27 to 0.33
e) 0.33 to 0.39
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
54. A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _______.
a) 0.54 to 0.66
b) 0.59 to 0.61
c) 0.57 to 0.63
d) 0.52 to 0.68
e) 0.68 to 0.76
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
55. A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 90% confidence interval to estimate the population proportion. The resulting confidence interval is _______.
a) 0.546 to 0.654
b) 0.536 to 0.664
c) 0.596 to 0.604
d) 0.571 to 0.629
e) 0.629 to 0.687
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
56. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The point estimate for this population proportion is _______.
a) 0.150
b) 0.300
c) 0.182
d) 0.667
e) 0.786
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Easy
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
57. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 90% confidence interval for the population proportion is _________.
a) 0.108 to 0.192
b) 0.153 to 0.247
c) 0.091 to 0.209
d) 0.145 to 0.255
e) 0.255 to 0.265
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
58. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 95% confidence interval for the population proportion is _________.
a) 0.108 to 0.192
b) 0.153 to 0.247
c) 0.091 to 0.209
d) 0.101 to 0.199
e) 0.199 to 0.201
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
59. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 98% confidence interval for the population proportion is _________.
a) 0.108 to 0.192
b) 0.153 to 0.247
c) 0.091 to 0.209
d) 0.145 to 0.255
e) 0.250 to 0.275
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
60. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She randomly selects a sample of 200 households. Forty households prefer the new package to all other package designs. The point estimate for this population proportion is _______.
a) 0.20
b) 0.25
c) 0.40
d) 0.45
e) 0.55
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Easy
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
61. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She randomly selects a sample of 200 households. Forty households prefer the new package to all other package designs. The 90% confidence interval for the population proportion is _________.
a) 0.199 to 0.201
b) 0.153 to 0.247
c) 0.164 to 0.236
d) 0.145 to 0.255
e) 0.185 to 0.275
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
62. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Brian would like to minimize the variance of waiting time for these customers, since this would mean each customer received the same level of service. Accordingly, his staff recorded the waiting times for 15 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. Assume that waiting time is normally distributed. The 90% confidence interval for the population variance of waiting times is ________.
a) 9.46 to 34.09
b) 56.25 to 64.87
c) 11.05 to 16.03
d) 8.58 to 39.79
e) 12.50 to 42.35
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
63. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Brian would like to minimize the variance of waiting time for these customers, since this would mean each customer received the same level of service. Accordingly, his staff recorded the waiting times for 15 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. Assume that waiting time is normally distributed. The 95% confidence interval for the population variance of waiting times is ________.
a) 9.46 to 34.09
b) 56.25 to 64.87
c) 11.05 to 16.03
d) 8.58 to 39.79
e) 12.50 to 42.35
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
64. Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250 common stocks. Velma relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector. Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%. Assume that annualized returns are normally distributed. The 90% confidence interval for the population variance of annualized returns for utility stocks is _______.
a) 0.018 to 0.064
b) 0.016 to 0.078
c) 0.017 to 0.066
d) 0.016 to 0.075
e) 0.020 to 0.080
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
65. Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250 common stocks. Velma relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector. Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%. Assume that annualized returns are normally distributed. The 95% confidence interval for the population variance of annualized returns for utility stocks is _______.
a) 0.018 to 0.064
b) 0.016 to 0.078
c) 0.017 to 0.066
d) 0.016 to 0.075
e) 0.020 to 0.080
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
66. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff randomly selected personnel files for 10 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 5 hours. Assume that training times are normally distributed. The 90% confidence interval for the population variance of training times is ________.
a) 11.83 to 83.33
b) 2.37 to 16.67
c) 2.66 to 13.51
d) 13.30 to 67.67
e) 15.00 to 68.00
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
67. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff randomly selected personnel files for 10 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 5 hours. Assume that training times are normally distributed. The 95% confidence interval for the population variance of training times is ________.
a) 11.83 to 83.32
b) 2.37 to 16.67
c) 2.66 to 13.51
d) 13.30 to 67.57
e) 15.40 to 68.28
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
68. Given n = 17, s2 = 18.56, and that the population is normally distributed, the 80% confidence interval for the population variance is ________.
a) 11.4372 ≤ σ 2 ≤ 36.3848
b) 23.5418 ≤ σ 2 ≤ 9.31223
c) 12.6141 ≤ σ 2 ≤ 31.8892
d) 11.2929 ≤ σ 2 ≤ 37.2989
e) 14.2929 ≤ σ 2 ≤ 39.2989
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
69. Given n = 12, s2 = 44.90, and that the population is normally distributed, the 99% confidence interval for the population variance is ________.
a) 19.0391 ≤ σ 2 ≤ 175.2888
b) 23.0881 ≤ σ 2 ≤ 122.3495
c) 25.6253 ≤ σ 2 ≤ 103.0993
d) 18.4588 ≤ σ 2 ≤ 189.7264
e) 14.2929 ≤ σ 2 ≤ 139.2989
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
70. Given n = 20, s = 32, and that the population is normally distributed, the 90% confidence interval for the population variance is ________.
a) 645.45 ≤ σ 2 ≤ 1923.10
b) 599.36 ≤ σ 2 ≤ 2135.39
c) 592.23 ≤ σ 2 ≤ 2184.47
d) 652.01 ≤ σ 2 ≤ 1887.42
e) 642.09 ≤ σ 2 ≤ 3982.30
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
71. Suppose the fat content of a hotdog follows normal distribution. Ten random measurements give a mean of 21.77 and standard deviation of 3.69. The 90% confidence interval for the population variance of fat content of a hotdog is ________
a) 5.2 to 21.3
b) 7.2 to 36.9
c) 19.63 to 23.91
d) 19.85 to 23.69
e) 2.69 to 5.1
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
72. A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least _______.
a) 44
b) 62
c) 216
d) 692
e) 700
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
73. A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval. The estimate needs to be within 12 of the actual population mean. The population variance is estimated to be around 2500. The necessary sample size should be at least _______.
a) 15
b) 47
c) 54
d) 638
e) 700
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
74. In estimating the sample size necessary to estimate p, if there is no good approximation for the value of p available, the value of ____ should be used as an estimate of p in the formula.
a) 0.10
b) 0.50
c) 0.40
d) 1.96
e) 2.00
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
75. A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues. The researcher wants to estimate the population proportion with a 95% level of confidence. He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio. The researcher wants the estimate to have an error of no more than .03. The necessary sample size is at least _______.
a) 27
b) 188
c) 211
d) 897
e) 900
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
76. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages; she will accept a 0.05 error. Previous studies indicate that new packaging has an approximately 70% acceptance rate. The sample size should be at least _______.
a) 27
b) 59
c) 323
d) 427
e) 500
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
77. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. He plans to use a 95% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee e-mail is not business related. Elwin should sample _______ e-mail messages.
a) 323
b) 12
c) 457
d) 14
e) 100
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
78. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. He plans to use a 98% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee e-mail is not business related. Elwin should sample approximately _______ e-mail messages.
a) 323
b) 12
c) 456
d) 14
e) 100
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
79. A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues. The researcher wants to estimate the population proportion with a 90% level of confidence. He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio. The researcher wants the estimate to have an error of no more than .02. The approximate sample size is at least _______.
a) 29
b) 47
c) 298
d) 1421
e) 1500
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
80. An insurance company is interested in conducting a study to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The approximate sample size should be at least _______.
a) 1037
b) 160
c) 41
d) 259
e) 289
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
81. A researcher wants to estimate the percent of the population that uses the internet to stay informed on world news issues. The researcher wants to estimate the population proportion with a 98% level of confidence. He estimates from previous studies that at least 65% of the population stay informed on world issues through the internet. He also wants the error to be no more than .03. The approximate sample size should be at least _______.
a) 41
b) 313
c) 1677
d) 1373
e) 1500
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
82. A study is going to be conducted in which the mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. The estimate needs to be within +/- 2 hours of the actual population mean. The population standard deviation σ is estimated to be around 25. The necessary sample size should be at least _______.
a) 100
b) 21
c) 923
d) 35
e) 423
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
83. The z value associated with a two-sided 99% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
d) 2.576
e) 2.33
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Knowledge
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
84. The employees of Cybertronics Inc. need to complete a certification online. A random sample of 49 employees gives an average time for completion of all the coursework and passing the tests of 20 hours. Assume that the population standard deviation is 6 hours and the population of employees is fairly large. Construct a 95% confidence interval for the average time required to complete the certification.
a) 18.28 to 21.72
b) 18.32 to 21.68
c) 18.36 to 21.64
d) 18.40 to 21.60
e) 19.76 to 20.24
Response: See section 8.1 Estimating the Population Mean using the z Statistic (σ Known)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.1: Estimate the population mean with a known population standard deviation using the z statistic, correcting for a finite population if necessary.
85. The employees of Cybertronics Inc. need to complete a certification online. A random sample of 16 employees gives an average time for completion of all the coursework and passing the tests of 20 hours. The population standard deviation is unknown but the sample standard deviation is 6 hours. You can assume that the population of employees is fairly large. Construct a 95% confidence interval for the average time required to complete the certification.
a) 17.06 to 22.94
b) 16.80 to 23.20
c) 17.68 to 22.32
d) 17.99 to 22.01
e) 18.31 to 21.69
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation with the t statistic and properties of the t distribution.
86. The t score (or table value for Student’s t distribution) associated with the upper 5% and 48 degrees of freedom is ______.
a) 1.677
b) 1.687
c) 1.697
d) 1.707
e) 1.717
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.2 Estimate the population mean with an unknown population standard deviation with the t statistic and properties of the t distribution.
87. For a new product, you need to determine the average diameter of a specialized electronic component, which will be a critical component of the new product. You measure the diameter in a sample of size 15 and find an average diameter of 0.24 mm, with a standard deviation of 0.02 mm. Other studies indicate that the diameter of similar products is normally distributed. The 99% confidence interval for the average diameter of this electronic component is closest to ______.
a) 0.232 to 0.248
b) 0.230 to 0.250
c) 0.228 to 0.252
d) 0.225 to 0.255
e) 0.224 to 0.256
Response: See section 8.2 Estimating the Population Mean using the t Statistic (σ Unknown)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.2: Estimate the population mean with an unknown population standard deviation with the t statistic and properties of the t distribution.
88. A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method. For this purpose, she takes a random sample of 50 manufacturing companies and finds out that 28 of them employ this method. The point estimate for the proportion of the population that uses this method is ______.
a) 0.88
b) 0.56
c) 0.44
d) 0.28
e) 0.22
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
89. A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method. For this purpose, she takes a random sample of 50 manufacturing companies and finds out that 28 of them employ this method. The 95% confidence interval for the proportion of manufacturing companies that use six sigma is ______.
a) 0.462 to 0.628
b) 0.452 to 0.638
c) 0.442 to 0.648
d) 0.432 to 0.658
e) 0.422 to 0.698
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
90. A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method. For this purpose, she will take a random sample of 50 manufacturing companies and find out how many of them use this method. She estimates that the proportion will be anywhere from 0.4 to 0.55. Of all the proportions in that range, which one would produce the widest 95% confidence interval for the population proportion?
a) 0.4
b) 0.45
c) 0.5
d) 0.55
e) 0.6
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Hard
AACSB: Analysis
Bloom’s level: Application
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
91. A researcher wants to estimate the proportion of the manufacturing companies that use the six sigma method. For this purpose, she will take a random sample of 50 manufacturing companies and find out how many of them use this method. She estimates that the proportion will be anywhere from 0.4 to 0.55. Of all the proportions in that range, which one would produce the narrowest 95% confidence interval for the population proportion?
a) 0.4
b) 0.45
c) 0.5
d) 0.55
e) 0.6
Response: See section 8.3 Estimating the Population Proportion
Difficulty: Hard
AACSB: Analysis
Bloom’s level: Application
Learning Objective: 8.3: Estimate a population proportion using the z statistic.
92. You need to determine the population variance of the diameters of a specialized electronic component used for a new product. Other studies indicate that the diameters of this product are roughly normally distributed. You take a sample of 15 units and find out that the sample average diameter is 0.24 mm, and the sample standard deviation is 0.2 mm. What is the 95% confidence interval for the population variance?
a) 0.0214 to 0.0995
b) 0.0230 to 0.1066
c) 0.1466 to 0.3154
d) 0.1666 to 0.3354
e) 0.1866 to 0.3554
Response: See section 8.4 Estimating the Population Variance
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.4: Use the chi-square distribution to estimate the population variance given the sample variance.
93. If you need to estimate the population mean within 2.5 units and with a confidence level of 95%. The minimum value observed is 15 and the maximum, 65. What sample size would you use?
a) 9
b) 10
c) 81
d) 96
e) 97
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
94. A researcher wants to estimate the proportion of Millennials who regularly listen to podcasts (defined as at least two entire podcasts per week). Previous studies indicate that only 18% of Millennials listen regularly to podcasts, and this researcher wants to estimate if that figure has increased. For this purpose, the researcher will use a 98% confidence level and wants to estimate the population proportion within 0.05 (i.e., 5 percentage points) of the actual value. The approximate sample size is at least ______.
a) 47
b) 48
c) 318
d) 321
e) 331
Response: See section 8.5 Estimating the Sample Size
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 8.5: Determine the sample size needed in order to estimate the population mean and population proportion.
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Business Stats Contemporary Decision 10e | Test Bank by Ken Black
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