Two samples,each with n = 8,produce an independent-measures t statistic of t = -2.15.Which of the following decisions is justified for a two-tailed test?
A)Reject H0 with α = .05 but fail to reject with α = .01
B)Reject H0 with both α = .05 and α = .01
C)Fail to reject H0 with both α = .05 and α = .01
D)Fail to reject H0 with α = .05 but reject H0 with α = .01

Question

Quizplus · Accepted Answer

Since the t-statistic is negative, we know that the sample mean difference is negative. For a two-tailed test with n = 8 and alpha = .05, the critical t-value is approximately ±2.306. Since our calculated t-value of -2.15 falls within the critical range of -2.306 to +2.306, we fail to reject the null hypothesis with alpha = .05. However, for alpha = .01, the critical t-value is approximately ±3.355, which is outside our calculated t-value range, so we reject the null hypothesis with alpha = .01. Therefore, we can justify rejecting the null hypothesis with alpha = .01 but failing to reject it with alpha = .05. Choice A is the only option that reflects this conclusion.

Two Samples,each with N = 8,produce an Independent-Measures T Statistic