Reconsider the paint-drying situation of Example 8.2, 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 X¯) below the null value is ¯x = 72.3?

(b) If ¯x = 72.3, what is the conclusion using α = 0.002?

(c) For the test procedure with α = 0.002, what is β(70)?

(d) If the test procedure with α = 0.002 is used, what n is necessary to ensure that β(70) = 0.01? (e) If a level 0.01 test is used when n = 100, what is the probability of a type I error when µ = 76.