Is the mean lifetime of particular type of car engine greater than 350,000 km? To test this claim,a sample of 100 engines is measured,yielding an average of 354,585 km and a standard deviation of 18515 km.

A) Reject the null hypothesis of μ = 350,000 with a P-value of 0.0134.There is sufficient evidence that the mean engine lifetime is longer than 350,000 km.
B) Reject the null hypothesis of μ = 350,000 with a P-value of 0.0066.There is sufficient evidence that the mean engine lifetime is longer than 350,000 km.
C) Fail to reject the null hypothesis of μ = 350,000 with a P-value of 0.9934.There is not sufficient evidence that the mean engine lifetime is longer than 350,000 km.
D) Fail to reject the null hypothesis with a P-value of 0.0735.There is not sufficient evidence that the mean engine lifetime is longer than 350,000 km.
E) There is not enough information to perform the test.

Question

jasmine martinez · Accepted Answer

Final Answer : B, Explanation :  We can use a one-sample t-test to test this claim. The null hypothesis is that the true mean lifetime of the engine is 350,000 km and the alternative hypothesis is that the true mean is greater than 350,000 km.The test statistic is calculated as:t = (x̄ - μ) / (s / √n) = (354,585 - 350,000) / (18515 / √100) = 2.47Where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.Using a t-distribution with 99 degrees of freedom (100-1), the p-value for this test is 0.0066 (calculated using a two-tailed test, and doubling the p-value since this is a one-tailed test).Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. Therefore, there is sufficient evidence that the mean engine lifetime is longer than 350,000 km. The correct answer is B.

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