A machine that grinds valves is set to produce valves whose lengths have mean 100 mm and

Chapter 6, Problem 11

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A machine that grinds valves is set to produce valves whose lengths have mean 100 mm and standard devia- tion 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 \(\mu\) 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 \(H_{0}: \mu=100\) versus \(H_{1}: \mu \neq 100\).

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 \(H_0\) be rejected at the 5% level?

d. If the sample mean length is 100.01 mm, will \(H_0\) be rejected at the 10% level?

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

Equation Transcription:

Text Transcription:

mu

H_0:=100

H_1:mu{not=}100

H_0

H_0