Question

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness  of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by σ = 0.20 mm. Thicknesses of each sheet in a sample of sheets will be measured, and a test of the hypothesis H_0:μ≤4 versus H_1:μ>4 will be performed. Assume that, in fact, the true mean thickness is 4.04 mm.

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

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

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

d) If 100 sheets are sampled, and the rejection region is X ̅≥4.02, what is the power of the test?

Answer 1

Answer:

Given that:

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by = 0.20 mm.

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

If

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

If

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

If

d) If 100 sheets are sampled, and the rejection region is   what is the power of the test?

If