Question

We perform a two-tailed, one-sample t-test of the null hypothesis that the true population mean is 63, versus the alternative hypothesis that the mean is different from 63. We find a test statistic of T=−1.12 (df = 499), with a p-value of 0.264. What is our decision about the null hypothesis at an alpha = 0.05?

a. Reject the null hypothesis
b. Fail to reject the null hypothesis
c. Insufficient information to decide

Answer 1

The p-value of 0.264 is greater than the alpha level of 0.05, so we fail to reject the null hypothesis in the one-sample t-test.

Step-by-step explanation:

When we perform a two-tailed, one-sample t-test, we compare the obtained p-value to the chosen alpha level (\(\alpha\)) to decide whether to accept or reject the null hypothesis. With an alpha of 0.05 and a p-value of 0.264, we compare the values and find that the p-value is greater than alpha (p-value > \(\alpha\)). Therefore, based on the result of the t-test, we fail to reject the null hypothesis that the true population mean is 63, because the evidence is not sufficient to conclude that the mean is significantly different from 63.