Reconsider the previous two exercises. Change the significance level to 0.10 (with a sample size of 100 at-bats), and answer Questions (a) to (d). Then describe the effect of decreasing the significance level on the power of the test.

Date from previous exercise

a. Open the Power Simulation applet. Enter 0.250 for the hypothesized value, 0.333 for the alternative value, and 20 for the sample size. Enter 200 for the number of samples, and click on Draw Samples. Repeat four more times to produce a total of 1,000 simulated samples. Comment on how much overlap you see between the two distributions. Does this overlap suggest that it’s easy or difficult to distinguish between a .250 hitter and a .333 hitter in a sample of 20 at-bats?
b. Choose the Level of Significance option, and enter 0.05 for the significance level. Click on Count. The top graph indicates how many hits the player needs in 20 at-bats in order to produce a p-value less than 0.05 to provide convincing evidence to reject the null hypothesis that his success probability is 0.250. How many hits are needed?

c. Based on the bottom graph, in what proportion of the 1,000 samples will the player with a 0.333 probability of success obtain enough hits to reject the hypothesis that he has a 0.250 probability of success? Th is is the approximate power of the test.

d. Would you say that the player has a good chance of convincing the manager that he has improved in a sample of 20 at-bats? Write a summary, as if to the player.