For Exercises 7.1 and 7.2, see page 360; for 7.3 and 7.4, see page 362; for 7.5 to 7.7, see page 365; for 7.8 and 7.9, see page 368; for 7.10 and 7.11, see page 371; and for 7.12 and 7.13, see page 372.

Question 7.7

7.7 Average quarterly return.

A stockbroker determines the short-run direction of the market using the average quarterly return of stock mutual funds. He believes the next quarter will be profitable when the average is greater than 1%. He will get complete quarterly return information soon, but right now he has data from a random sample of 30 stock funds. The mean quarterly return in the sample is 1.5%, and the standard deviation is 1.9%. Based on this sample, test to see if the broker will feel the next quarter will be profitable.

  1. State appropriate null and alternative hypotheses. Explain how you decided between the one- and two-sided alternatives.
  2. Find the statistic, degrees of freedom, and -value. State your conclusion using the significance level.

7.7

(a) . Because the next quarter will be profitable when the average is greater than 1%, this indicates a one-sided alternative. (b) . The data do not give good evidence that the next quarter will be profitable.