Let denote the mean diameter for bearings of a certain type. A test of H0:

Let µ denote the mean diameter for bearings of a certain type. A test of H0: µ = 0.5 versus Ha: µ = 0.5 will be based on a sample of n bearings. The diameter distribution is believed to be normal. Determine the value of b in each of the following cases:
a. n = 15, a = .05, σ = 0.02, µ = 0.52
b. n = 15, a = .05, σ = 0.02, µ = 0.48
c. n = 15, a = .01, σ = 0.02, µ = 0.52
d. n = 15, a = .05, σ = 0.02, µ = 0.54
e. n = 15, a = .05, σ = 0.04, µ = 0.54
f. n = 20, a = .05, σ = 0.04, µ = 0.54
g. Is the way in which b changes as n, a, s, and µ vary consistent with your intuition? Explain.