# Mathematics

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

53) In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct the 90% confidence interval for the population proportion, p? Explain.

53) _____________

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

54) A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6%? 54) _______

A) 378 B) 10 C) 755 D) 267

55) A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 4%? 55) _______

A) 423 B) 256 C) 11 D) 846

56) A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%? 56) _______

A) 1068 B) 752 C) 2135 D) 17

57) A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6%? A previous study indicates that the proportion of left-handed golfers is 10%. 57) _______

A) 166 B) 136 C) 185 D) 38

58) A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%? A previous study indicates that the proportion of households with two cars is 24%. 58) _______

A) 281 B) 198 C) 369 D) 4

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

59) A state highway patrol official wishes to estimate the number of drivers that exceed the speed limit traveling a certain road.

a) How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 2%?

b) Repeat part (a) assuming previous studies found that 85% of drivers on this road exceeded the speed limit. 59) _____________

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

60) Find the critical values, X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.95 and n = 12. 60) _______

A) 3.816 and 21.920 B) 3.053 and 24.725

C) 4.575 and 26.757 D) 2.603 and 19.675

61) Find the critical values, X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.90 and n = 15. 61) _______

A) 6.571 and 23.685 B) 4.075 and 31.319

C) 4.660 and 29.131 D) 5.629 and 26.119

62) Find the critical values, X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.98 and n = 20. 62) _______

A) 7.633 and 36.191 B) 6.844 and 27.204

C) 8.907 and 38.582 D) 10.117 and 32.852

63) Find the critical values, X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.99 and n = 10. 63) _______

A) 1.735 and 23.587 B) 2.156 and 25.188

C) 2.088 and 21.666 D) 2.558 and 23.209

64) Construct a 95% confidence interval for the population standard deviation s of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 12.4 pounds. Assume the population is normally distributed. 64) _______

A) ( 9.1, 19.6) B) ( 82.4, 382.4) C) ( 2.6, 5.6) D) ( 9.5, 18.1)

65) Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 2.6 inches. Construct a 99% confidence interval for the population standard deviation, s. 65) _______

A) ( 1.8, 4.7) B) ( 1.8, 4.8) C) ( 1.1, 2.9) D) ( 1.8, 4.4)

66) Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 1.4 inches. Construct a 98% confidence interval for the population variance, sigma to power of (2). 66) _______

A) ( 1.0, 4.9) B) ( 1.0, 2.2) C) ( 0.7, 3.5) D) ( 1.1, 5.1)

67) The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 2.7 years. Construct the 98% confidence interval for the population variance, sigma to power of (2). Assume the data are normally distributed 67) _______

A) ( 3.2, 26.3) B) ( 1.8, 5.1) C) ( 1.2, 9.7) D) ( 3.1, 22.5)

68) A student randomly selects 10 CDs at a store. The mean is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, s. Assume the data are normally distributed. 68) _______

A) ($1.03, $2.74) B) ($0.43, $1.32)

C) ($1.43, $2.70) D) ($1.76, $3.10)

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

69) The heights (in inches) of 20 randomly selected adult males are listed below. Construct a 99% confidence interval for the variance, sigma to power of (2). Assume the population is normally distributed.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72 69) _____________

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

70) The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation, s. Assume the data are normally distributed.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 70) _______

A) (0.81, 1.83) B) (0.32, 0.85) C) (0.53, 1.01) D) (1.10, 2.01)

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

71) A container of car oil is supposed to contain 1000 milliliters of oil. A quality control manager wants to be sure that the standard deviation of the oil containers is less than 20 milliliters. He randomly selects 10 cans of oil with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of s. Does this confidence interval suggest that the variation in the oil containers is at an acceptable level? 71) _____________