ch08_Operations Research Solution

CHAPTER EIGHT

Statistical Inference: Estimation for Single Populations

B 1. When a statistic calculated from sample data is used to estimate a population parameter, it is called _______.

M A. an interval estimateTerm B. a point estimate

C. a statistical parameterD. a good guess

A 2. When a range of values is used to estimate a population parameter, it is called _______.

E A. an interval estimateTerm B. a point estimate

C. a statistical parameterD. a range estimate

201

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A 3. 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 prefer the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using a _______.

M A. a point estimateBApp B. a range estimate

C. a statistical parameterD. an interval estimate

D 4. 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 ________.

M A. a range estimateBApp B. a statistical parameter

C. an interval estimateD. a point estimate

C 5. 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 MaintenanceMean 7.5Standard

Deviation

1.5

If Eugene concludes that the average rate of “ease of maintenance” for all customers is 7.5, he is using ________.

Chapter 8: Statistical Inference: Estimation for Single Populations 203

M A. arange estimateBApp B. a statistical parameter

C. a point estimateD. an interval estimate

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A 6. 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 “efficiency of operation” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). His staff assembled the following statistics.

Efficiency of Operation

Mean 6.0Standard

Deviation

2.5

If Eugene concludes that the average rate of “efficiency of operation” for all customers is 6.0, he is using ________.

M A. a point estimateBApp B. a statistical parameter

C. a range estimateD. an interval estimate

D 7. Mary Flindt, a Marketing Director with Epsilon Airlines, is assessing the relative importance of the "total flight" experience. An item on a survey questionnaire distributed to 100 of Epsilon's customers asked them to rate the importance of “on-time arrival” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). Her staff assembled the following statistics from the responses.

On-time ArrivalMean 9.1Standard

Deviation

2.5

If Mary concludes that the average rate of “on-time arrival” for all customers is 9.1, she is using ________.

M A. an interval estimateBApp B. a statistical parameter


C. a range estimateD. a point estimate

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D 8. Mary Flindt, a Marketing Director with Epsilon Airlines, is assessing the relative importance of the "total flight" experience. An item on a survey questionnaire distributed to 100 of Epsilon's customers asked them to rate the importance of “cabin space” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). Her staff assembled the following statistics from the responses.

Cabin SpaceMean 7.2Standard

Deviation

3.7

If Mary concludes that the average rate of “cabin space” for all customers is 7.2, she is using ________.

M A. an interval estimateBApp B. a statistical parameter

C. a range estimateD. a point estimate

B 9. The Z value associated with a two-sided 90% confidence interval is _______.

E A. 1.28Calc B. 1.645

C. 1.96D. 2.575

C 10. The Z value associated with a two-sided 95% confidence interval is _______.

E A. 1.28Calc B. 1.645

C. 1.96D. 2.575


E A. 1.645Calc B. 1.28


C. 0.84D. 0.29

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E A. 1.28Calc B. 1.55

C. 1.17D. 0.88

D 13. The Z value associated with a two-sided 92% confidence interval is _______.

E A. 1.41Calc B. 0.92

C. 0.46D. 1.75


E A. 1.41Calc B. 1.34

C. 0.46D. 1.75

D 15. 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 _______.

M A. 94.08 to 101.92Calc B. 92.85 to 103.15

C. 97.35 to 98.65D. 93.34 to 102.66

A 16. 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 _______.

M A. 94.71 to 101.29Calc B. 97.45 to 98.55

C. 94.08 to 101.92D. 97.35 to 98.65


C 17. Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 95% confidence interval for the population mean is _______.

M A. 94.71 to 101.29Calc B. 97.45 to 98.55

C. 94.08 to 101.92D. 97.35 to 98.65

C 18. Suppose a random sample of size 64 is selected from a population. The sample yields a mean of 26 and a standard deviation of 4. From this information, the 90% confidence interval to estimate the population mean can be computed to be _______.

M A. 25.36 to 26.64Calc B. 25.92 to 26.08

C. 25.18 to 26.82D. 25.90 to 26.10

B 19. 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 and that the standard deviation was 4 minutes. The 90% confidence interval for the population mean of waiting times is ________.

M A. 14.27 to 15.73BCalc B. 14.06 to 15.94

C. 9.88 to 20.12D. 13.86 to 16.14

A 20. 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 and that the standard deviation was 4 minutes. The 95% confidence interval for the population mean of waiting times is ________.

M A. 13.88 to 16.12BCalc B. 7.16 to 22.84

C. 14.06 to 15.94

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D. 8.42 to 21.58


D 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 64 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. The 88% confidence interval for the population mean of waiting times is ________.

M A. 8.80 to 21.20BCalc B. 14.33 to 15.67

C. 10.30 to 19.70D. 14.11 to 15.89

B 22. 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 and that the standard deviation was 5 hours. The 88% confidence interval for the population mean of training times is ________.

M A. 17.25 to 32.75BCalc B. 24.23 to 25.78

C. 24.42 to 25.59D. 19.15 to 30.85

D 23. 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 and that the standard deviation was 5 hours. The 92% confidence interval for the population mean of training times is ________.

M A. 16.25 to 33.75BCalc B. 24.30 to 25.71

C. 17.95 to 32.05D. 24.13 to 25.99

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C 24. 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 and that the standard deviation was 5 hours. The 95% confidence interval for the population mean of training times is ________.

M A. 15.20 to 34.80BCalc B. 24.18 to 25.82

C. 24.02 to 25.98D. 16.78 to 33.23

B 25. 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 121 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.


Deviation

1.1

The 90% confidence interval for the population mean rating of “ease of maintenance” is ________.

M A. 5.34 to 9.66BCalc B. 7.34 to 7.66

C. 5.69 to 9.31D. 7.30 to 7.70


D 26. 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 121 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.


Deviation

1.1

The 95% confidence interval for the population mean rating of “ease of maintenance” is ________.

M A. 5.34 to 9.66BCalc B. 7.34 to 7.66

C. 5.69 to 9.31D. 7.30 to 7.70

A 27. Mary Flindt, a Marketing Director with Epsilon Airlines, is assessing the relative importance of the "total flight" experience. An item on a survey questionnaire distributed to 100 of Epsilon's customers asked them to rate the importance of “cabin space” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). Her staff assembled the following statistics from the responses.


Deviation

3.7

The 95% confidence interval for the population mean rating of “cabin space” is ________.

M A. 6.47 to 7.93BCalc B. 0.00 to 14.45

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C. 0.00 to 6.47D. 6.47 to 14.45


C 28. Mary Flindt, a Marketing Director with Epsilon Airlines, is assessing the relative importance of the "total flight" experience. An item on a survey questionnaire distributed to 121 of Epsilon's customers asked them to rate the importance of “cabin space” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). Her staff assembled the following statistics from the responses.


Deviation

3.7

The 99% confidence interval for the population mean rating of “cabin space” is ________.

M A. 0.00 to 7.39BCalc B. 0.00 to 14.45

C. 6.33 to 8.07D. 6.47 to 14.45

A 29. A random sample of 64 items is selected from a population of 400 items. The sample mean is 200 and the sample standard deviation is 48. From this data, a 95% confidence interval to estimate the population mean can be computed as _______.

M A. 189.21 to 210.79Calc B. 188.24 to 211.76

C. 190.13 to 209.87D. 190.94 to 209.06

D 30. A random sample of 64 items is selected from a population of 400 items. The sample mean is 200 and the sample standard deviation is 48. From this data, a 90% confidence interval to estimate the population mean can be computed as _______.

M A. 189.21 to 210.79Calc B. 188.24 to 211.76

C. 190.13 to 209.87D. 190.94 to 209.06

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A 31. A researcher wants to estimate the proportion of the population which possess a given characteristic. A random sample of size 600 is taken resulting in 330 items which possess the characteristic. The point estimate for this population proportion is _______.

E A. 0.55Calc B. 0.33

C. 0.60D. 0.45

C 32. The normal distribution is used to test about a population mean for large samples. "Large" is usually defined as _______.

E A. at least 100Term B. at least 5% of the population size

C. at least 30D. at least 12

B 33. The t test was developed by _______.

E A. Charles StudentTerm B. William Gosset

C. deMoivreD. Gauss

C 34. The t-distribution is similar to a normal distribution. However the t-distribution is _______.

M A. not symmetricTerm B. bimodal

C. flatterD. discrete

B 35. The t-distribution is similar to a normal distribution. However the t-distribution is a _______.

M A. leptokurtic distributionTerm B. platykurtic distribution

C. mesopotamian distributionD. discrete distribution


B 36. In order to find values in the t distribution table, you must convert the sample size or sizes to _______.

E A. population sizesTerm B. degrees of freedom

C. Z valuesD. student values

A 37. If the degrees of freedom in a t distribution get very large, _______.

M A. the t values and the Z values are almost the sameTerm B. the sample size must be very small

C. the population size must be very largeD. the sample mean approaches zero

B 38. The table t value associated with the upper 5% of the t distribution and 12 degrees of freedom is _______.

E A. 2.179Calc B. 1.782

C. 1.356D. 3.055

D 39. The table t value associated with the upper 5% of the t distribution and 14 degrees of freedom is _______.

E A. 2.977Calc B. 2.624

C. 2.145D. 1.761

A 40. The table t value associated with the upper 10% of the t distribution and 23 degrees of freedom is _______.

E A. 1.319Calc B. 1.714

C. 2.069D. 1.321

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B 41. The table t value associated with the upper 1% of the t distribution and 5 degrees of freedom is _______.

E A. 4.032Calc B. 3.365

C. 3.747D. 1.476

A 42. The table t value associated with the upper 10% of the t distribution and 17 degrees of freedom is _______.

E A. 1.333Calc B. 1.337

C. 1.740D. 2.567

D 43. The table t value associated with the upper 5% of the t distribution and 15 degrees of freedom is _______.

E A. 2.947Calc B. 2.602

C. 2.131D. 1.753

A 44. The table t value associated with the upper 0.5% of the t distribution and 4 degrees of freedom is _______.

E A. 4.604Calc B. 2.776

C. 2.132D. 2.353

B 45. The table t value associated with 10 degrees of freedom and used to compute a 95% confidence interval is _______.

E A. 1.812Calc B. 2.228

C. 3.169D. 1.372



E A. 3.055Calc B. 2.179

C. 1.782D. 1.796


E A. 1.323Calc B. 1.721

C. 2.080D. 2.518

C 48. The table t value associated with 8 degrees of freedom and used to compute a 99% confidence interval is _______.

E A. 1.397Calc B. 1.860

C. 3.355D. 2.896

C 49. 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 _______.

E A. 18Calc B. 17

C. 16D. 15

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C 50. 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 ______________.

M A. 118.99 to 119.11BCalc B. 118.82 to 119.28

C. 118.98 to 119.12D. 118.85 to 119.25

A 51. 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 ______________.

M A. 118.99 to 119.11BCalc B. 118.87 to 119.23

C. 119.00 to 119.10D. 118.89 to 119.21

B 52. 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 _________.

M A. 1.76 to 2.66BCalc B. 2.01 to 2.41

C. 2.08 to 2.34D. 1.93 to 2.49

D 53. 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 _________.

M A. 63.37 to 86.63BCalc B. 61.60 to 88.41

C. 71.77 to 78.23D. 71.28 to 78.72


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C 54. 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 _________.

M A. 66.78 to 83.23BCalc B. 72.72 to 77.28

C. 72.53 to 77.47D. 66.09 to 83.91

B 55. A researcher wants to estimate the proportion of the population which possess 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 _______.

E A. 0.55Calc B. 0.45

C. 0.35D. 0.65

A 56. A researcher wants to estimate the proportion of a population which possess a given characteristic. A random sample of size 250 is taken and 40% of the sample possess the characteristic. The 90% confidence interval to estimate the population proportion is _______.

M A. 0.35 to 0.45Calc B. 0.34 to 0.46

C. 0.37 to 0.43D. 0.39 to 0.41

B 57. A researcher wants to estimate the proportion of a population which possess a given characteristic. A random sample of size 250 is taken and 40% of the sample possess the characteristic. The 95% confidence interval to estimate the population proportion is _______.

M A. 0.35 to 0.45Calc B. 0.34 to 0.46

C. 0.37 to 0.43D. 0.39 to 0.41


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C 58. A researcher wants to estimate the proportion of a population which possess a given characteristic. A random sample of size 200 is taken and 30% of the sample possess the characteristic. The 95% confidence interval to estimate the population proportion is _______.

M A. 0.53 to 0.67Calc B. 0.25 to 0.35

C. 0.24 to 0.36D. 0.27 to 0.33

B 59. A researcher wants to estimate the proportion of a population which possess a given characteristic. A random sample of size 200 is taken and 30% of the sample possess the characteristic. The 90% confidence interval to estimate the population proportion is _______.

M A. 0.53 to 0.67Calc B. 0.25 to 0.35

C. 0.24 to 0.36D. 0.27 to 0.33

D 60. 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 _______.

M A. 0.54 to 0.66Calc B. 0.59 to 0.61

C. 0.57 to 0.63D. 0.52 to 0.68

A 61. 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 _______.

M A. 0.546 to 0.654Calc B. 0.536 to 0.664

C. 0.596 to 0.604D. 0.571 to 0.629


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A 62. 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 _______.

E A. BApp B. 0.300

C. 0.182D. 0.667

A 63. 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 _________.

M A. 0.108 to 0.192BCalc B. 0.153 to 0.247

C. 0.091 to 0.209D. 0.145 to 0.255

D 64. 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 _________.

M A. 0.108 to 0.192BCalc B. 0.153 to 0.247

C. 0.091 to 0.209D. 0.101 to 0.199

C 65. 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 _________.

M A. 0.108 to 0.192BCalc B. 0.153 to 0.247

C. 0.091 to 0.209D. 0.145 to 0.255


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A 66. 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 _______.

M A. 0.20BCalc B. 0.25

C. 0.40D. 0.45

B 67. 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 _________.

M A. 0.199 to 0.201BCalc B. 0.153 to 0.247

C. 0.164 to 0.236D. 0.145 to 0.255

C 68. 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 95% confidence interval for the population proportion is _________.

M A. 0.153 to 0.247BCalc B. 0.199 to 02.01

C. 0.145 to 0.255D. 0.198 to 0.202

C 69. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at the AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The point estimate for this population proportion is _______.

M A. 0.0002BCalc B. 16.670


C. 0.0600D. 0.0333

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A 70. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at the AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The 90% confidence interval for the population proportion is _________.

M A. 0.043 to 0.077BCalc B. 0.046 to 0.074

C. 0.039 to 0.081D. 0.028 to 0.060

D 71. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at the AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The 95% confidence interval for the population proportion is _________.

M A. 0.043 to 0.077BCalc B. 0.046 to 0.074

C. 0.028 to 0.060D. 0.039 to 0.081

A 72. 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 variance was 4 minutes. The 90% confidence interval for the population variance of waiting times is ________.

M A. 9.46 to 34.09BCalc B. 56.25 to 64.87

C. 11.05 to 16.03D. 8.58 to 39.79


D 73. 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 variance was 4 minutes. The 95% confidence interval for the population variance of waiting times is ________.

M A. 9.46 to 34.09BCalc B. 56.25 to 64.87

C. 11.05 to 16.03D. 8.58 to 39.79

C 74. 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%. The 90% confidence interval for the population variance of annualized returns is _______.

M A. 0.018 to 0.064BCalc B. 0.016 to 0.078

C. 0.017 to 0.066D. 0.016 to 0.075

B 75. 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%. The 95% confidence interval for the population variance of annualized returns is _______.

M A. 0.018 to 0.064BCalc B. 0.016 to 0.078

C. 0.017 to 0.066D. 0.016 to 0.075

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D 76. 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. The 90% confidence interval for the population variance of training times is ________.

M A. 11.83 to 83.33BCalc B. 2.37 to 16.67

C. 2.66 to 13.51D. 13.30 to 67.57

A 77. 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. The 95% confidence interval for the population variance of training times is ________.

M A. 11.83 to 83.33BCalc B. 2.37 to 16.67

C. 2.66 to 13.51D. 13.30 to 67.57

B 78. The finite correction factor should be used if the sample size is _______.

M A. less than 5% of the population sizeTerm B. more than 5% of the population size

C. less than 30D. more than 100

B 79. In finding a confidence interval for the population mean, the population standard deviation should be used if it is known. If the population standard deviation is not known, then it should be estimated with _______.

E A. the sample varianceTerm B. the sample standard deviation

C. the rangeD. the mean


A 80. What proportion of a population possesses a given characteristic? To estimate this, a random sample of 1700 people are interviewed from the population. Seven hundred and fourteen of the people sampled possess the characteristic. Using this information, the researcher computes an 88% confidence interval to estimate the proportion of the population who possess the given characteristic. The resulting confidence interval is _______.

M A. 0.401 to 0.439Calc B. 0.409 to 0.431

C. 0.392 to 0.448D. 0.389 to 0.451

A 81. In estimating the sample size necessary to estimate a population mean, the error of estimation, E, is equal to _______.

E A. the distance between the sample mean and the population mean

Term B. the distance between the sample mean and the varianceC. the Z scoreD. the sample size

B 82. In estimating sample size, if the population standard deviation is unknown, it can be estimated by using _______.

M A. the population meanTerm B. one-fourth of the range

C. one-half of the rangeD. the Z score

C 83. Suppose a researcher wants to conduct a study to estimate the population mean. He plans to use a 95% level of confidence to estimate the mean, and the population standard deviation is approximately 34. The researcher wants the error to be no more than 4. The sample size should be at least _______.

M A. 7Calc B. 196

C. 278D. 1110

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B 84. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. He plans to use a 95% confidence interval estimate of mean training time of tellers and is willing to accept an error of 1 hour; previous studies indicated a standard deviation of 2 hours. The sample size should be at least _______.

M A. 4BCalc B. 16

C. 34D. 68

B 85. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. He plans to use a 90% confidence interval estimate of mean training time of tellers and is willing to accept an error of 1 hour; previous studies indicated a standard deviation of 5 hours. The sample size should be at least _______.

M A. 4BCalc B. 16

C. 34D. 68

A 86. 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 _______.

M A. 44Calc B. 62

C. 216D. 692

C 87. 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 _______.

M A. 15Calc B. 47


C. 53D. 638

B 88. 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.

E A. 0.10Term B. 0.50

C. 0.40D. 1.96

D 89. 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 _______.

M A. 27Calc B. 188

C. 211D. 897

C 90. 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 _______.

M A. 27BCalc B. 59

C. 323D. 427

B 91. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She plans to use a 80% 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

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approximately 70% acceptance rate. The sample size should be at least _______.

M A. 27BCalc B. 59

C. 323D. 427


A 92. 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.

E A. BApp B. 12

C. 457D. 14

C 93. 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 _______ e-mail messages.

E A. BApp B. 12

C. 457D. 14

D 94. 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 _______.

M A. 29Calc B. 47

C. 298D. 1421

A 95. 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 _______.

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M A. 1036Calc B. 160

C. 41D. 259

D 96. 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 _______.

M A. 41Calc B. 313

C. 1677D. 1373

B 97. You wish to determine the proportion of all secretaries who are familiar with a particular word processing package. You will conduct a random survey. How large a sample should you take if you want to be 95% confident of the results and within 0.05 of the true population proportion?

M A. 73Calc B. 384

C. 95D. 277

C 98. You wish to determine the proportion of all secretaries who are familiar with a particular word processing package. You will conduct a random survey. How large a sample should you take if you want to be 90% confident of the results and within 0.04 of the true population proportion?

M A. 152Calc B. 216

C. 423D. 600

B 99. A bank officer wishes to estimate the amount of the average total deposits per customer at the bank. She wishes the estimate to be within $200 of the actual average with 95%


confidence. She assumes the standard deviation for this should be $1000. How large should the sample be?

M A. 10BCalc B. 96

C. 68D. 19,208

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B 100. A bank officer wishes to estimate the amount of the average total deposits per customer at the bank. She wishes the estimate to be within $100 of the actual average with 90% confidence. She assumes the standard deviation for this should be $800. How large should the sample be?

M A. 51BCalc B. 173

C. 246D. 17,318


101. While evaluating the service level provided to walk-in customers, Brian Vanecek, VP of Operations at Portland Trust Bank, encountered resistance to some of his proposals from fellow executives. Brian focuses on providing timely, efficient service to the banks customers; customers having to wait for service upsets him; and some customers share his philosophy, but not all. The VP of Marketing points out that some customers (for various reasons) "don't want to rush in and out." Moreover, the bank's management wants to provide a warm friendly atmosphere for customers.

Identify some potential segments of the bank's walk-in customers. (Are drive-through customers a distinct segment?) How can a statistical analysis of walk-in customers help identify and evaluate service alternatives for the segments? What estimates are needed?

M _________________________________________________________________ BApp _________________________________________________________________

_________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________

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102. Stockton Steel, Inc. can qualify for a lucrative contract to supply steel rods if it can meet the buyer’s process capability requirements. Specifically, the buyer requires documented evidence that the standard deviation of Stockton's process is no more than 1/12th of the difference between the upper tolerance limit and the lower tolerance limit, £ (UTL - LTL)/12.

Sarah Shum, Director of Quality Programs, is assigned the task of developing the documentation. She knows that variability of the rod length depends on several factors: the operators' skill, the mix used in the steel melt, the quality of materials used in the mix, and the condition of the equipment.

Discuss Sarah's assignment. What estimates does she need? Which departments must participate in the process capability study? Which of these departments will not participate after completion of the study?

M _________________________________________________________________ BApp _________________________________________________________________

_________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________


103. Alan Lessoff, VP of Marketing at CyberWarehouse, Inc. (CWI), wants to learn more about online shoppers that visit the CyperWarehouse web sites.

Identify some potential segments of the CWI's online shoppers. (Are repeat-visitors a distinct segment?) How can a statistical analysis of online shoppers help identify and evaluate service alternatives, merchandise selection, and web site design for the segments? What estimates are needed?

MBApp

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104. Online financial brokerages continue go grow with the Internet. CyberMarkets, Inc. (CMI) advises e-commerce businesses on their marketing strategies.

Addalie McMinn, VP of Research at CMI, expects increasingly intense competition between online brokerages for new customers as the industry matures. She wants to learn more about the customers of online brokerages; she wants to understand "what makes them tick" so she can advise CMI clients how to compete more successfully. What factors do these investors use to choose one broker over another? Transaction costs? Basic service characteristics such as fast order execution, and timely, well-organized statements? Free tie-in services such as an address book, a calendar service, and links to favorite web sites for gifts.

Should Addalie segment the customer population? Are all factors equally important for all market segments? Does age, gender, or professional occupation matter?

How can a statistical analysis of online brokerage customers assist with stategy formulation? Describe the statistical methods that will be useful to Addalie during the study. What estimates are needed?

MBApp

Documents

ch08_Operations Research Solution