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Homework answers / question archive / 1)When a statistic calculated from sample data is used to estimate a population parameter, it is called a point estimate
1)When a statistic calculated from sample data is used to estimate a population parameter, it is called a point estimate.
2. When a range of values is used to estimate a population parameter, it is called a range estimate.
3. If the population is not normal but its standard deviation, s is known and the sample size, n is large (n ≥ 30), zdistribution values may be used to determine interval estimates for the population mean.
4. If the population is normal and its standard deviation, s, is known but the sample size is small, zdistribution values may not be used to determine interval estimates for the population mean.
5. When the population standard deviation, s, is unknown the sample standard deviation, s, is used in determining the interval estimate for the population mean.
6. If the population is normal and its standard deviation, s, is known and the sample size, n, is large (n ≥ 30), interval estimates for the population mean must be determined using zvalues.
7. An assumption underlying the use of tstatistic in samplebased estimation is that the population is normally distributed.
8. A tdistribution is similar to a normal distribution, but with flatter tails.
9. In order to find values in the t distribution table, you must determine the appropriate degrees of freedom based on the sample sizes.
10. If the degrees of freedom in a t distribution increase, difference between the t values and the z values will also increase.
11. In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the values from a tdistribution rather than the zdistribution.
12. In determining the interval estimates for a population variance using the sample variance, it is appropriate to use the values from a chisquare distribution rather than a tdistribution.
13. 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 population mean
14. Use of the chisquare statistic to estimate the population variance is extremely robust to the assumption that the population is normally distributed.
15. Like a tdistribution, a chisquare distribution is symmetrical and extends from minus infinity to plus infinity.
Multiple Choice
16. 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) a point estimate
b) a range estimate
c) a statistical parameter
d) an interval estimate
e) an exact estimate
17. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walkin customers. Accordingly, his staff recorded the waiting times for 45 randomly selected walkin customers, and calculated that their mean waiting time was 15 minutes. If Brian concludes that the average waiting time for all walkin 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 99% confidence interval to estimate the population mean is _______.
a) 94.08 to 101.92
b) 92.85 to 103.15
c) 97.35 to 98.65
d) 93.34 to 102.66
e) 90.20 to 105.00
24. Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 90% confidence interval for the population mean is _______.
a) 94.71 to 101.29
b) 97.45 to 98.55
c) 94.08 to 101.92
d) 97.35 to 98.65
e) 95.00 to 105.00
25. Suppose a random sample of size 64 is selected from a population yielding a sample mean of 26. The population standard deviation is 4. From this information, the 90% confidence interval to estimate the population mean can be computed to be _______.
a) 25.36 to 26.64
b) 25.92 to 26.08
c) 25.18 to 26.82
d) 25.90 to 26.10
e) 26.00 to 27.80
26. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walkin customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walkin 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
27. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walkin customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walkin 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
28. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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) 24.23 to 25.78
c) 24.42 to 25.59
d) 19.15 to 30.85
e) 21.00 t0 32.00
29. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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
30. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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
31. 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 this data, a 95% confidence interval to estimate the population mean can be computed as _______.
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
32. 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 this data, a 90% confidence interval to estimate the population mean can be computed as _______.
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
33. The normal distribution is used to test about 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
34. 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
35. 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)
36. 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
37. A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. 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
38. The lengths of steel rods produced by a shearing process are normally distributed. A random sample of 10 rods is selected; the sample mean length is 119.05 inches; and the sample standard deviation is 0.10 inch. The 95% confidence interval for the population mean rod length is ______________.
a) 118.99 to 119.11
b) 118.82 to 119.28
c) 118.98 to 119.12
d) 118.85 to 119.25
e) 119.89 to 122.12
39. The lengths of steel rods produced by a shearing process are normally distributed. A random sample of 10 rods is selected; the sample mean length is 119.05 inches; and the sample standard deviation is 0.10 inch. The 90% confidence interval for the population mean rod length is ______________.
a) 118.99 to 119.11
b) 118.87 to 119.23
c) 119.00 to 119.10
d) 118.89 to 119.21
e) 119.21 to 123.87
40. 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
41. 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
42. 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
43. 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
44. 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
45. A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 250 is taken and 40% of the sample possesses the characteristic. The 90% 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 0.45
46. A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 250 is taken and 40% of the sample possesses the characteristic. 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
47. A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 200 is taken and 30% of the sample possesses the characteristic. 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
48. A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 200 is taken and 30% of the sample possesses the characteristic. 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
49. 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
50. 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
51. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. A random sample of 200 email 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
52. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. A random sample of 200 email 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
53. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. A random sample of 200 email 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
54. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. A random sample of 200 email 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
55. 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
56. 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
57. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walkin 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 walkin 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
58. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walkin 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 walkin 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
59. 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 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
60. 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 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
61. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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 67.57
e) 15.00 to 68.00
62. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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 83.33
b) 2.37 to 16.67
c) 2.66 to 13.51
d) 13.30 to 67.57
e) 15.40 to 68.28
63. Given n = 17, s^{2} = 18.56, and that the population is normally distributed, the 80% confidence interval for the population variance is ________.
a) 11.4372 £ s ^{2} £ 36.3848
b) 23.5418 £ s ^{2} £ 9.31223
c) 12.6141 £ s ^{2} £ 31.8892
d) 11.2929 £ s ^{2} £ 37.2989
e) 14.2929 £ s ^{2} £ 39.2989
64. Given n = 12, s^{2} = 44.90, and that the population is normally distributed, the 99% confidence interval for the population variance is ________.
a) 19.0391 £ s ^{2} £ 175.2888
b) 23.0881 £ s ^{2} £ 122.3495
c) 25.6253 £ s ^{2} £ 103.0993
d) 18.4588 £ s ^{2} £ 189.7279
e) 14.2929 £ s ^{2} £ 139.2989
65. Given n = 20, s = 32, and that the population is normally distributed, the 90% confidence interval for the population variance is ________.
a) 645.4458 £ s ^{2} £ 1923.0986
b) 599.3635 £ s ^{2} £ 2135.3859
c) 592.2258 £ s ^{2} £ 2184.4685
d) 652.0129 £ s ^{2} £ 1887.4185
e) 642.0929 £ s ^{2} £ 3982.2989
66. 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
67. 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) 53
d) 638
e) 700
68. 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
69. A researcher wants to estimate the population proportion with a 95% level of confidence. He estimates from previous studies that the population proportion is no more than .30. 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
70. 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
71. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. He plans to use a 95% confidence interval estimate of the proportion of email messages that are nonbusiness; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee email is not business related. Elwin should sample _______ email messages.
a) 323
b) 12
c) 457
d) 14
e) 100
72. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS email for nonbusiness communications. He plans to use a 98% confidence interval estimate of the proportion of email messages that are nonbusiness; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee email is not business related. Elwin should sample _______ email messages.
a) 323
b) 12
c) 457
d) 14
e) 100
73. A researcher wants to estimate the population proportion with a 90% level of confidence. She estimates from previous studies that the population proportion is no more than .30. The researcher wants the estimate to have an error of no more than .02. The necessary sample size is at least _______.
a) 29
b) 47
c) 298
d) 1421
e) 1500
74. A study will be conducted to estimate the population proportion. 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 size of sample should be at least _______.
a) 1036
b) 160
c) 41
d) 259
e) 289
75. A researcher conducts a study to determine what the population proportion is for a given characteristic. It is believed from previous studies that the proportion of the population will be at least .65. The researcher wants to use a 98% level of confidence. He also wants the error to be no more than .03. The sample size should be at least _______.
a) 41
b) 313
c) 1677
d) 1373
e) 1500
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