Resistors for use in a certain application are supposed to have a mean resistance greater than

Resistors for use in a certain application are supposed to have a mean resistance μ greater than 100 Ω. Assume that the standard deviation of the resistances is 5 Ω. Resistances will be measured for a sample of resistors, and a test of the hypothesis H₀ :μ ≤ 100 versus H₁ :μ > 100 will be made. Assume that in fact the true mean resistance is 101Ω.

a. If 100 resistors are sampled, what is the power of a test made at the 5% level?

b. How many resistors must be sampled so that a 5% level test has power 0.95?

c. If 100 resistors are sampled, at what level must the test be made so that the power is 0.90?

d. If 100 resistors are sampled, and the rejection region is X̅ > 100.5, what is the power of the test?