Question: Using the data provided in problem, test the null hypothesis that returns on the investment are normally distributed, but with unknown mean and standard deviation. That is, test only for the validity of the normal-distribution assumption. How is this test different from the one in problem?
Problem: Returns on an investment have been known to be normally distributed with mean 11% (annualized rate) and standard deviation 2%. A brokerage firm wants to test the null hypothesis that this statement is true and collects the following returns data in percent (assume a random sample):
8, 9, 9.5, 9.5, 8.6, 13, 14.5, 12, 12.4, 19, 9, 10, 10, 11.7, 15, 10.1, 12.7, 17, 8, 9.9, 11, 12.5, 12.8, 10.6, 8.8, 9.4, 10, 12.3, 12.9, 7.
Conduct the analysis and state your conclusion.