A paired-samples t test results in the following statistic: t(6) = 2.41.Using this test result, what decision should be made about a two-tailed hypothesis test at p = 0.05?
A) Reject the null hypothesis and conclude the mean difference is greater than expected.
B) Reject the null hypothesis and conclude a strong effect size.
C) Fail to reject the null hypothesis because the sample size is too low to achieve statistical power.
D) Fail to reject the null hypothesis because the test statistic does not exceed the critical cutoff.

Question

Quizplus · Accepted Answer

The t-test result gives us the t-statistic and the degrees of freedom (df). In this case, the t-statistic is 2.41 and the df is 6.

To make a decision about the null hypothesis being true or false, we need to compare the t-statistic to a critical value based on the chosen alpha level and the df.

In this case, the alpha level is 0.05 and we have a two-tailed hypothesis test. With df=6, the critical value for a two-tailed test at alpha=0.05 is ±2.447.

Since the absolute value of our t-statistic (2.41) is less than the critical value (2.447), we fail to reject the null hypothesis. We cannot conclude that the mean difference is greater than expected or that there is a strong effect size. We simply do not have enough evidence to say that the null hypothesis is false. Therefore, the correct choice is D, fail to reject the null hypothesis because the test statistic does not exceed the critical cutoff.

A Paired-Samples T Test Results in the Following Statistic: T(6)