Question

An independent-measures research study uses two samples, a total of 23 participants in both samples combined....

An independent-measures research study uses two samples, a total of 23 participants in both samples combined. If the data produce a t statistic of t = 2.10, then which of the following is the correct decision for a two-tailed hypothesis test?

 Cannot answer without additional information Reject the null hypothesis with a = .05 but fail to reject with a = .01. Reject the null hypothesis with either a = .05 or a = .01. Fail to reject the null hypothesis with either a = .05 or a = .01.

Solution:

Here we have given that, the test is independent two sample t-test.

n1=n2 =23 and the test statistics = 2.10 and the test is two tailed test.

Assuming that the variances are not equal , we use degrees of freedom of unpooled test,so

df = smaller of (n1-1)and (n2-1) = 22

Then by using T table , with alpha = 0.01 and df = 22,we get critical value tc = 2.819

So decision: Here test statistics t(2.10) < critical value tc,so we fail to reject Ho.

Then with alpha =0.05 and df =22.we get criticla value tc = 2.074

So decision:Here test statistics t(2.10) > critical value tc, so we reject Ho.

Therefore here correct option is 2.Reject the null hypothesis with a = .05 but fail to reject with a = .01.