Use Table 4 in the Appendix to obtain L

5.58 Refer to Exercise 5.57. The lobbyist for the business group has his expert examine the experimental equipment and determines that there may be measurement errors in recording the reaction times. Unless the difference in reaction time is at least .25 seconds, the expert claims that the two times are essentially equivalent.

a. Is there sufficient evidence that the median difference in reaction time is greater than

.25 seconds?

b. What other factors about the drivers are important in attempting to decide whether

moderate consumption of alcohol affects reaction time? Soc. 5.59 In an attempt to increase the amount of money people would receive at retirement from Social Security, the U.S. Congress during its 1999 session debated whether a portion of Social Security funds should be invested in the stock market. Advocates of mutual stock funds reassure the public by stating that most mutual funds would provide a larger retirement income than the income currently provided by Social Security. The annual rates of return of two highly recom- mended mutual funds for the years 1989 through 1998 are given here. The annual rate of return is defined as P 1 ⫺ P 兾P , where P and P 1 are the prices of the fund at the beginning and end of the year, respectively. Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Fund A 25.4 17.1 ⫺ 8.9 26.7 3.6 ⫺ 8.5 ⫺ 1.3 32.9 22.9 26.6 Fund B 31.9 ⫺ 8.4 41.8 6.2 17.4 ⫺ 2.1 30.5 15.8 26.8 5.7

a. For both fund A and fund B, estimate the mean and median annual rate of return and

construct a 95 confidence interval for each.

b. Which of the parameters, the mean or median, do you think best represents the

annual rate of return for fund A and for fund B during the years 1989 through 1998? Justify your answer. 5.60 Refer to Exercise 5.59. a. Is there sufficient evidence that the median annual rate of return for the two mutual funds is greater than 10?

b. Is there sufficient evidence that the mean annual rate of return for the two mutual

funds is greater than 10? 5.61 What other summaries of the mutual fund’s rate of return are of importance to a person selecting a retirement plan? 5.62 Using the information in Table 5.8, answer the following questions. a. If the population has a normal distribution, then the population mean and median are identical. Thus, either the mean or median could be used to represent the center of the population. In this situation, why is the t test more appropriate than the sign test for testing hypotheses about the center of the distribution?

b. Suppose the population has a distribution that is highly skewed to the right. The

researcher uses an a ⫽ .05 t test to test hypotheses about the population mean. If the sample size n ⫽ 10, will the probability of a Type I error for the test be .05? Justify your answer.

c. When testing hypotheses about the mean or median of a highly skewed population, the

difference in power between the sign and t test decreases as the size of M a ⫺ M increases. Verify this statement using the values in Table 5.8. Why do think this occurs?

d. When testing hypotheses about the mean or median of a lightly skewed population,

the difference in power between the sign and t test is much less than that for a highly skewed population distribution. Verify this statement using the values in Table 5.8. Why do you think this occurs? Supplementary Exercises H.R. 5.63 An office manager has implemented an incentive plan that she thinks will reduce the mean time required to handle a customer complaint. The mean time for handling a complaint was 30 minutes prior to implementing the incentive plan. After the plan was in place for several