The lifetime of a certain type of car engine is normally distributed with a mean of 200,000 miles and a standard deviation of 30,000 miles. An automaker claims that the new-year model has an engine with a longer average lifetime. A sample of 16 cars with this type of engine from the new model is obtained for a test. Consider a rejection region { ≥ 215,000}. a) What hypotheses should be tested? b) Find the probability of a type 1 error. c) Suppose that a further study establishes that, in fact, the average lifetime of the new engine is 210,000 miles. Find the probability of a type II error. Show your reasoning.

The lifetime of a certain type of car engine is normally distributed with a mean of 200,000 miles and a standard deviation of 30,000 miles. An automaker claims that the new-year model has an engine with a longer average lifetime. A sample of 16 cars with this type of engine from the new model is obtained for a test. Consider a rejection region { ≥ 215,000}. a) What hypotheses should be tested? b) Find the probability of a type 1 error. c) Suppose that a further study establishes that, in fact, the average lifetime of the new engine is 210,000 miles. Find the probability of a type II error. Show your reasoning.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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