Simulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15.

(a) Test the null hypothesis H0: µ = 100 versus H1: µ ≠ 100 for each of the 100 simple random samples.

(b) If we test this hypothesis at the α = 0.05 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) Describe how we know that a rejection of the null hypothesis results in making a Type I error in this situation.