A machine that grinds valves is set to produce valves whose lengths have mean 100 mm and standard deviation 0.1 mm. The machine is moved to a new location. It is thought that the move may have upset the calibration for the mean length, but that it is unlikely to have changed the standard deviation. Let μ represent the mean length of valves produced after the move. To test the calibration, a sample of 100 valves will be ground, their lengths will be measured, and a test will be made of the hypotheses H₀ : μ = 100 versus H₁ : μ ≠ 100.

a. Find the rejection region if the test is made at the 5% level.

b. Find the rejection region if the test is made at the 10% level.

c. If the sample mean length is 99.97 mm, will H₀ be rejected at the 5% level?

d. If the sample mean length is 100.01 mm, will H₀ be rejected at the 10% level?

e. A critical point is 100.015 mm. What is the level of the test?