46. Identify the following:

1. [latex]\displaystyle\overline{x}[/latex]=_______
2. sx =_______
3. n =_______
4. n – 1 =_______

47. Define the random variables X and [latex]\displaystyle\overline{X}[/latex] in words.

48. Which distribution should you use for this problem?

49. Construct a 95% confidence interval for the population mean time spent waiting. State the confidence interval, sketch the graph, and calculate the error bound.

50. Explain in complete sentences what the confidence interval means.

51. Identify the following:

1. [latex]\overline{x}[/latex]=_______
2. sx =_______
3. n =_______
4. n – 1 =_______

52. Define the random variable X in words.

53. Define the random variable [latex]\displaystyle\overline{X}[/latex]

in words.

54. Which distribution should you use for this problem?

55. Construct a 99% confidence interval for the population mean hours spent watching television per month. (a) State the confidence interval, (b) sketch the graph, and (c) calculate the error bound.

56. Why would the error bound change if the confidence level were lowered to 95%?

57. Calculate the following:

1. [latex]\displaystyle\overline{x}[/latex]=______
2. sx =______
3. n =______

58. Define the random variable [latex]\displaystyle\overline{X}[/latex] in words.

59. What is [latex]\displaystyle\overline{x}[/latex] estimating?

60. Is [latex]{\sigma}_{x}[/latex] known?

61. As a result of your answer to 60, state the exact distribution to use when calculating the confidence interval.

62. How much area is in both tails (combined)?

63. How much area is in each tail?

65. The 95% confidence interval is_____.

66. Fill in the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean.

67. In one complete sentence, explain what the interval means.

68. Using the same [latex]\displaystyle\overline{x}[/latex], sx, and level of confidence, suppose that n were 69 instead of 39. Would the error bound become larger or smaller? How do you know?

72. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.

1. 1. [latex]\displaystyle\overline{x}[/latex]= __________
   2. sx = __________
   3. n = __________
   4. n – 1 = __________
2. Define the random variables X and[latex]\displaystyle\overline{X}[/latex] in words.
3. Which distribution should you use for this problem? Explain your choice.
4. Construct a 95% confidence interval for the population mean time wasted.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
5. Explain in a complete sentence what the confidence interval means.

73. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

1. 1. x⎯⎯ = __________
   2. sx = __________
   3. n = __________
   4. n – 1 = __________
2. Define the random variable X in words.
3. Define the random variable X⎯⎯⎯ in words.
4. Which distribution should you use for this problem? Explain your choice.
5. Construct a 95% confidence interval for the population mean length of time.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
6. What does it mean to be “95% confident” in this problem?

74. Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of three months. Assume that the underlying population distribution is normal.

1. 1. [latex]\displaystyle\overline{x}[/latex] = __________
   2. sx = __________
   3. n = __________
   4. n – 1 = __________
2. Define the random variable X in words.
3. Define the random variable[latex]\displaystyle\overline{X}[/latex] in words.
4. Which distribution should you use for this problem? Explain your choice.
5. Construct a 99% confidence interval for the population mean length of time using training wheels.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
6. Why would the error bound change if the confidence level were lowered to 90%?

75. The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative) to raise money to help other candidates’ campaigns.

76. The FEC has reported financial information for 556 Leadership PACs that operating during the 2011–2012 election cycle. The following table shows the total receipts during this cycle for a random selection of 20 Leadership PACs.

[latex]\overline{x}=\$251,854.23[/latex]

s= $521,130.41

Use this sample data to construct a 96% confidence interval for the mean amount of money raised by all Leadership PACs during the 2011–2012 election cycle. Use the Student’s t-distribution.

77. Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table shows the ages of the corporate CEOs for a random sample of these firms.

78. Use this sample data to construct a 90% confidence interval for the mean age of CEO’s for these top small firms. Use the Student’s t-distribution.

79. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.

1. 1. [latex]\displaystyle\overline{X}[/latex] = __________
   2. sx = __________
   3. n = __________
   4. n-1 = __________
2. Define the random variables X and X⎯⎯⎯ in words.
3. Which distribution should you use for this problem? Explain your choice.
4. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.

80. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.

1. Which distribution should you use for this problem? Explain your choice.
2. Define the random variable X⎯⎯⎯ in words.
3. Construct a 95% confidence interval for the population mean cost of a used car.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
4. Explain what a “95% confidence interval” means for this study.

81. Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Assume the underlying distribution is approximately normal.

1. Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
2. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?
3. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.
4. Calculate the mean.
5. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?

82. A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

1. 1. x⎯⎯ = __________
   2. sx = __________
   3. n = __________
   4. n-1 = __________
2. Define the random variables X and X⎯⎯⎯ in words.
3. Which distribution should you use for this problem? Explain your choice.
4. Construct a 95% confidence interval for the population mean worth of coupons.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
5. If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why.

84. Find the 95% Confidence Interval for the true population mean for the amount of soda served.

1. (12.42, 14.18)
2. (12.32, 14.29)
3. (12.50, 14.10)
4. Impossible to determine

85. What is the error bound?

1. 0.87
2. 1.98
3. 0.99
4. 1.74

Use the following information to answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions.

Use the following information to answer the next five exercises: Suppose the marketing company did do a survey. They randomly surveyed 200 households and found that in 120 of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions.

Use the following information to answer the next five exercises: Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as mid-level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.

Use the following information to answer the next five exercises: A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Use the following information to answer the next 16 exercises: The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

112. Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample proportion.

Use the following information to answer the next three exercises: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 surveyed) feel that “education and our schools” is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education and the schools is one of the top issues facing California.

Use the following information to answer the next two exercises: Five hundred and eleven (511) homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three (173) of the homes surveyed met the minimum recommendations for earthquake preparedness, and 338 did not.