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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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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