Exercise Solution 4.8

The power of our tests is the probability of their rejecting the null hypothesis that the coin is fair. That probability depends, of course, on the unknown parameter p. The .05 significance level test rejects the null hypothesis if s falls outside the interval [41, 60]. If p equals 0.50, 0.48 or 0.40, the power of the test is 0.046, 0.072 or 0.543, respectively. Based on our solution for Exercise 4.7, the  .01 significance level test rejects the null hypothesis if s falls outside the interval [37, 62]. If p equals 0.50, 0.48 or 0.40, the power of the test is 0.009, 0.012 or 0.239, respectively. Calculations are presented in a downloadable spreadsheet.