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A tire company claims the lifetimes of its tires average 50,000 miles. The standard deviation of lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypotheses that the mean tire lifetime is 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500. c) If the test is made at the 5% level, what is the power?

A tire company claims the lifetimes of its tires average 50,000 miles. The standard deviation of lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypotheses that the mean tire lifetime is 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500. c) If the test is made at the 5% level, what is the power?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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3. A tire company claims the lifetimes of its tires average 50,000 miles. The standard deviation of lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypotheses that the mean tire lifetime is 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500. c) If the test is made at the 5% level, what is the power? d) At what level should the test be conducted so that the power is .80? e) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is .80 if the test is made at the 5% level?
Transcribed Image Text:3. A tire company claims the lifetimes of its tires average 50,000 miles. The standard deviation of lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypotheses that the mean tire lifetime is 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500. c) If the test is made at the 5% level, what is the power? d) At what level should the test be conducted so that the power is .80? e) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is .80 if the test is made at the 5% level?
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