Question

An independent-measures research study uses two samples, each with n = 15 participants. If the data produce a t statistic of t = 2.760, which of the following is the correct decision for a two-tailed hypothesis test?a. Reject the null hypothesis with α = .05 but fail to reject with α = .01

b. Reject the null hypothesis with either α = .05 or α = .01

c .Fail to reject the null hypothesis with either α = .05 or α = .01

d .Cannot answer without additional information

Answer 1

The correct decision for a two-tailed hypothesis test with a t statistic of t = 2.760 and two independent samples depends on the significance level (alpha) chosen for the test. If alpha is .05, the null hypothesis is rejected, but if alpha is .01, the null hypothesis is not rejected. Both options a and c are correct, depending on the chosen significance level.

Step-by-step explanation:

The correct decision for a two-tailed hypothesis test with a t statistic of t = 2.760 and two samples, each with n = 15 participants, depends on the significance level (alpha) chosen for the test. Let's consider the options provided:

1. a. Reject the null hypothesis with alpha = .05 but fail to reject with alpha = .01
2. b. Reject the null hypothesis with either alpha = .05 or alpha = .01
3. c. Fail to reject the null hypothesis with either alpha = .05 or alpha = .01
4. d. Cannot answer without additional information

If the significance level (alpha) is .05, the correct decision would be option a. Reject the null hypothesis with alpha = .05 but fail to reject with alpha = .01. This is because the t-value of 2.760 is greater than the critical t-value for a two-tailed test at alpha = .05, but it is not greater than the critical t-value for alpha = .01. Therefore, we reject the null hypothesis at alpha = .05, but fail to reject at alpha = .01.

However, if the significance level (alpha) is .01, the correct decision would be option c. Fail to reject the null hypothesis with either alpha = .05 or alpha = .01. This is because the t-value of 2.760 is not greater than the critical t-value for a two-tailed test at either alpha = .05 or alpha = .01. Therefore, we fail to reject the null hypothesis at both alpha levels.