Reconsider the paint-drying situation of Example 8.5, in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H0: μ = 75 versus Ha: μ < 75 are to be tested using a random sample of n = 25 observations.
a. How many standard deviations (of ) below the null value is  = 72.3?
b. If  = 72.3, what is the conclusion using α = .002?
c. For the test procedure with α = .002, what is β(70)?
d. If the test procedure with α = .002 is used, what n is necessary to ensure that β(70) = .01?
e. If a level .01 test is used with n = 100, what is the probability of a type I error when μ = 76?