For a hypothesis test with a specified significance level a, the probability of a type I error is α, whereas the probability β of a type II error depends on the particular value of p that is used as an alternative to the null hypothesis.

a. Using an alternative hypothesis of p < 0.4, a sample size of n = 50, and assuming that the true value of p is 0.25, find the power of the test. See Exercise 36 in Section 8-2.

b. Find the value of b, the probability of making a type II error.

c. Given the conditions cited in part (a), what do the results indicate about the effectiveness of the hypothesis test?