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?

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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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