Question

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 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 9 of them are worn out. With this data, we test the following hypotheses at the 5% significance level. The P-value is 0.15

H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

Which of the following conclusions is correct?

A. Accept H0.
B. Fail to reject H0.
C. Reject H0.

Answer 1

Fail to reject H₀

Explanation:

To reject the null hypothesis, the P-value must be less than 0.05.

Since the P-value is 0.15 which is greater than 0.05, we would fail to reject the null hypothesis as there is no sufficient evidence against the null hypothesis.

Thus, the conclusion would be to fail to reject H₀.