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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? Reject H0. Fail to reject H0. Accept H0.

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? Reject H0. Fail to reject H0. Accept H0.

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Solution

Based on the given p-value of 0.15, which is greater than the significance level of 0.05, we fail to reject the null hypothesis (H0). This means that the data does not provide strong enough evidence to support the alternative hypothesis (Ha). Therefore, the conclusion is "Fail to reject H0".

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