This exercise can be done individually or, better yet, as a class project. For the pretzel packaging hypothesis test in Example 9.1 on page 342, the null and alternative hypotheses are, respectively, H0: μ = 454 g (machine is working properly) Ha: μ ≠ 454 g (machine is not working properly), where μ is the mean net weight of all bags of pretzels packaged.
The net weights are normally distributed with a standard deviation of 7.8 g.
a. Assuming that the null hypothesis is true, simulate 100 samples of 25 net weights each.
b. Suppose that the hypothesis test is performed at the 5% significance level. Of the 100 samples obtained in part (a), roughly how many would you expect to lead to rejection of the null hypothesis? Explain your answer.
c. Of the 100 samples obtained in part (a), determine the number that lead to rejection of the null hypothesis.
d. Compare your answers from parts (b) and (c), and comment on any observed difference.