Question

A sample of 14 from an approximately normal population is used to test H0: µ = 5 versus H1: µ > 5. If the p-value of this test is 0.0329, which of the following is the correct decision and conclusion at the α = 0.05 level?

a)Reject the null hypothesis concluding that there is no evidence the true mean is larger than 5.

b)Do not reject the null hypothesis concluding that there is evidence the true mean is larger than 5.

c)Reject the null hypothesis concluding that there is evidence that the true mean is larger than 5.

d)Do not reject the null hypothesis concluding that there is no evidence the true mean is larger than 5.

Answer 1

Rejecting the null hypothesis because the p-value is less than alpha indicates statistically significant evidence that the true population mean is greater than 5.

Step-by-step explanation:

Considering the provided information, where the p-value of the test is 0.0329 and the level of significance, alpha, is 0.05, we should compare the p-value to alpha in order to make a decision about the null hypothesis. Since the p-value (0.0329) is less than the alpha level (0.05), we reject the null hypothesis.

Hypothesis testing in this context is meant to determine if there is evidence to support that the population mean is greater than a certain value (in this case, 5). Because the p-value is less than alpha, it indicates that there is statistically significant evidence to conclude that the true population mean is indeed greater than 5.

Therefore, the correct decision and conclusion at the alpha = 0.05 level is: c) Reject the null hypothesis concluding that there is evidence that the true mean is larger than 5.