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. h₁: 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. accept h₀. c. fail to reject h₀.

Explanation:

Step1: Recall p - value decision rule

In hypothesis testing, if the p - value is greater than the significance level $\alpha$, we fail to reject the null hypothesis $H_0$.

Step2: Compare p - value and significance level

We are given that the significance level $\alpha = 0.05$ and the p - value $= 0.15$. Since $0.15>0.05$.

Answer:

C. Fail to reject $H_0$