8.29 and the Normal distribution. Consider the binomial setting with n = 40. You are testing the null hypothesis that p = 0.4 versus the two-sided alternative with a 5% chance of rejecting the null hypothesis when it is true.

1. (a) Find the values of the sample proportion that will lead to rejection of the null hypothesis.

2. (b) Repeat part (a) assuming a sample size of n = 80.

3. (c) Make a sketch illustrating what you have found in parts (a) and (b). What does your sketch show about the effect of the sample size in this setting?