Reconsider the paint-drying problem discussed in Example 8.5. The hypotheses were H0: = 75 versus Ha:

Reconsider the paint-drying problem discussed in Example 8.5. The hypotheses were H0: μ = 75 versus Ha: μ < 75, with s assumed to have value 9.0. Consider the alternative value μ = 74, which in the context of the problem would presumably not be a practically significant departure from H0.
a. For a level .01 test, compute β at this alternative for sample sizes n = 100, 900, and 2500.
b. If the observed value of  is  = 74, what can you say about the resulting P-value when n = 2500? Is the data statistically significant at any of the standard values of α?
c. Would you really want to use a sample size of 2500 along with a level .01 test (disregarding the cost of such an experiment)? Explain.