Reconsider the paint-drying problem discussed in Example 8.2. The hypotheses were H0: μ...

Reconsider the paint-drying problem discussed in Example 8.2. The hypotheses were H₀: μ = 75 versus H_a: μ < 75, with σ 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 b at this alternative for sample sizes n = 100, 900, and 2500.

b. If the observed value of is , 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.