1. An investment analyst has data for the past 8 years on each of two mutual funds, with the annual rates of return for each listed in file XR11074. On average, each fund has had an excellent annual rate of return over the time period for his data, but the analyst is concerned that a mutual fund with greater variation in rate of return tends to involve greater risk for his investment clients. Using the 0.05 level in a nondirectional test, examine whether the two mutual funds have differed significantly in their performance variability.
Reminder: Be sure to refer to Figure 11.1 in selecting the testing procedure for an exercise. When either test can be applied to the same data, the unequal-variances t-test is preferable to the z-test- especially when doing the test with computer assistance.
2. Suspecting that television repair shops tend to charge women more than they do men, Emily discon- nected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of
$28. Her friend John, taking the same set to another sam- ple of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Assuming normal populations with equal standard deviations, use the 0.05 level in evaluating Emily's suspicion. Using the appropriate statistical table, what is the approximate p-value for this test?