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 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? a. reject h₀. b. fail to reject h₀. c. accept h₀.

Explanation:

Step1: Recall decision - rule for hypothesis testing

In hypothesis testing at a significance level $\alpha$, if the p - value is greater than $\alpha$, we fail to reject the null hypothesis $H_0$. If the p - value is less than $\alpha$, we reject $H_0$. Here, the significance level $\alpha = 0.05$ and the p - value is $p=0.15$.

Step2: Compare p - value and significance level

Since $0.15>0.05$ (i.e., $p > \alpha$).

Answer:

B. Fail to reject $H_0$.