Question: A supplier to FORD claims that the treadlife of its tires has a mean of 32,000 miles. FORD is concerned that the actual performance may be less than claimed.

1. State suitable null and alternative hypotheses to test this claim.
   FORD randomly selects 25 vehicles, puts new tires on them, and runs them around the
   FORD test track until the tires need replacement. If M i is the mileage of the i th
   Vehicle’s tires,
   \[\sum\limits_{i=1}^{25}{{{M}_{i}}}=794,000\]
   \[\sum\limits_{i=1}^{25}{M_{i}^{2}}=25,230,249,473\]
2. What is the sample mean of the mileage?
3. What is the sample variance of the mileage?
4. What is the standard error of the average mileage?
5. Calculate a 90% confidence interval for the mean mileage.
6. Test the hypothesis you formulated, clearly state your conclusion about H0 from
   part (a) at the α0.05 level, and justify that conclusion. Drawing a picture may help.
7. If the true mean treadlife is actually 31,500 miles, what

is the probability of making a Type II error given the hypothesis you formulated and with

α0.05 ? Recall that a Type II error occurs when a false null hypothesis is not rejected.

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