Question

ch 20 a tire manufacturer claims that one particular type of tire will last at least 50,000 miles. a group of angry customers does not believe this is so. they took a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. if 0.0100 < p - value < 0.0200, what decision should be made if testing at the alpha = 0.05 level? do not reject ho and conclude that the tires were not performing as claimed. reject ho and conclude that the mean tire life really is 50,000 miles. reject ho and conclude that the tires were not performing as claimed. do not reject ho and conclude that the mean tire life really is 50,000 miles.

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the P - value < α (significance level), we reject the null hypothesis \(H_0\). Here, the significance level \(\alpha = 0.05\), and \(0.0100<\text{P - value}<0.0200\). Since \(0.0100<0.0200 < 0.05\), the P - value is less than \(\alpha\).

Step2: Interpret the null and alternative hypotheses

The null hypothesis \(H_0:\mu\geq50000\) (the tire manufacturer's claim) and the alternative hypothesis \(H_1:\mu < 50000\) (customers' claim). When we reject \(H_0\), we have evidence in favor of \(H_1\).

Answer:

Reject \(H_0\) and conclude that the tires were not performing as claimed.