Two samples each with n8 produce an independentmeasures t st

Two samples, each with n=8, produce an independent-measures t statistic of t = -2.12 in a two-tailed hypothesis test. Which of the following decisions is justified?

Fail to reject the null hypothesis with alpha = 0.05 but reject the null hypothesis with alpha = 0.01.

Reject the null hypothesis with either alpha=0.05 or alpha=0.01.

Fail to reject the null hypothesis with either alpha=0.05 or alpha=0.01.

Reject the null hypothesis with alpha=0.05 but fail to reject with alpha=0.01.

Solution

As

df = n1 + n2 - 2 = 8 + 8 - 2 = 14, then we see that the P value of a two tailed test with t = -2.12 is, using technology,

P = 0.05235683

Thus, as this is greater than both 0.05 and 0.01,

OPTION D: Fail to reject the null hypothesis with either alpha=0.05 or alpha=0.01.