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 objective of this question is to test the automaker's claim that the new-year model has an…

Answered: The lifetime of a certain type of car…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

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