A machine manufactures bolts that are supposed to be 3

Chapter 6, Problem 13SE

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A machine manufactures bolts that are supposed to be 3 inches in length. Each day a quality engineer selects a random sample of 50 bolts from the day’s production, measures their lengths, and performs a hypothesis test of \(H_0:\mu=3\) versus \(H_1:\mu \ne 3\), where \(\mu\) is the mean length of all the bolts manufactured that day. Assume that the population standard deviation for bolt lengths is 0.1 in. If \(H_0\) is rejected at the 5% level, the machine is shut down and recalibrated.

a. Assume that on a given day, the true mean length of bolts is 3 in. What is the probability that the machine will be shut down? (This is called the false alarm rate.)

b. If the true mean bolt length on a given day is 3.01 in., find the probability that the equipment will be recalibrated.

Equation Transcription:

Text Transcription:

H_0:mu=3

H_1:mu{not=}3

mu

H_0

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