Chapter 4 Homework

Question 33. The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard deviation of 8.2 hours. a. Using the sample data, construct a 99% confidence interval for the population mean.

z = +/- 2.68

68.6 – 2.68 * 8.2 / √50 = 65.49
68.6 + 2.68 * 8.2 / √50 = 71.71 b. Does the 99% confidence interval include the value suggested by the NCAA? Interpret this result.

Yes, the 99% confidence interval includes the value suggested by the NCAA, which is 70. Therefore the result makes sense.

c. Suppose you decided to switch from a 99% to a 95% confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?

Switching the confidence interval to 95% would decrease width of the interval and therefore the z level will be smaller than the +/-2.68 determined with the 99% confidence interval.

Question 42. As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants 14 failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10% of the applicants are now failing the test?
14/220 = 0.64 InvNorm = 2.5758
Standard Error = 2.5758 * √(0.64 * 0.36 / 220) = 0.08336
CI 99% = 0.64 – 0.08336 < u < 0.64 + 0.08336
CI 99% = 0.5566 < u < 0.7234 It is not be reasonable to conclude that more than 10% of the applicants are now failing the test.

Question 50. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an