A tire manufacturer has a 60000 mile warranty for tread life

A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 8% are worn out at 60,000 miles.

The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 15 of them are worn out. With this data, we test the following hypotheses at the 5% significance level.

H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.08.

Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.08.

The P-value is 0.15. Which conclusion is correct?

Accept H0.

Fail to reject H0.

Reject H0.

Solution

Since P-value is 0.15 which is larger than 0.05, we do not reject the null hypothesis.

Answer: Fail to reject H0.