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 100 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.
(a) State appropriate null and alternative hypotheses. Explain how you decided between the one- and two-sided alternatives.
(b) Find the test statistic, and its related P-value. State your conclusion using the 5% significance level.
(c) Using the normal distribution, compute the power of the test for 3 different values of the true mean: 0.5%, 2% and 3%.