Simulate drawing 100 simple random samples of size n = 40 from a population whose proportion is 0.3.

(a) Test the null hypothesis H0: p = 0.3 versus H1: p ≠ 0.3 for each simulated sample.

(b) If we test the hypothesis at the α = 0.1 level of significance, how many of the 100 samples would you expect to result in a Type I error?

(c) Count the number of samples that lead to a rejection of the null hypothesis. Is it close to the expected value determined in part (b)?

(d) How do we know that a rejection of the null hypothesis results in making a Type I error in this situation?