# Mean and Deviation

5.5.8 Let us say the life of a tire in miles, say X, is normally distributed with mean 0 and standard deviation 5000. Past experience indicates that 0=30,000. The manufacturer claims that the tires made by a new process have mean 0 >30,000. It is possible that 0=35,000. check his claim by testing H0: 0=30,000 against H1: 0 >30,000. We shall observe n independent values of X, say x1,...,xn, and we shall reject H0 iff xbar >= c. Determine n and c so that the power function y(0) of the test has the values y (30,000)=0.01 and y(35,000)=0.98.

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#### Solution Summary

5.5.8 Let us say the life of a tire in miles, say X, is normally distributed with mean 0 and standard deviation 5000. Past experience indicates that 0=30,000. The manufacturer claims that the tires made by a new process have mean 0 >30,000. It is possible that 0=35,000. check his claim by testing H0: 0=30,000 against H1: 0 >30,000. We shall observe n independent values of X, say x1,...,xn, and we shall reject H0 iff xbar >= c. Determine n and c so that the power function y(0) of the test has the values y (30,000)=0.01 and y(35,000)=0.98.