Hypothesis Testing: Critical Value for the Test Statistic

A statistical test performed on 100 observations yields a _t_-statistic of -2.5. The _strongest_ conclusion able to be drawn from these results is that the null hypothesis can be rejected at the:

Incorrect. The critical value for a two-tailed _t_-test using approximately 100 degrees of freedom is about $$\displaystyle t= \pm 2.63$$. A test statistic of _t_ = -2.5 is not in the critical region; it is in the acceptance region. So the null hypothesis could not be rejected at this level.

Correct. The critical values for t-tests with approximately 100 degrees of freedom be found on a t-table. The critical value at a given level of significance must be exceeded by this test statistic of -2.5 in absolute value in order to be rejected, and so you'll need the column which provides the highest critical value which is still below 2.5 here. That value is 2.364, which is found in the column of 0.01 for a one-tailed test. This is stronger than a 5% level of significance for a two-tailed test, which has a critical value of 1.984. The test can be rejected at this level as well, but since this is a weaker significance level, that doesn't satisfy the question. A significance level of 1% for a two-tailed test shows a critical value of 2.626, and the test cannot be rejected at this level.

Incorrect. A test statistic of _t_ = -2.5 is extreme enough to reject the null hypothesis at the 5% level. However, there is a stronger level of confidence that can also be drawn from this test.

1% level for a two-tailed test.

1% level for a one-tailed test.

5% level for a two-tailed test.