independent t test

Question

Which of the following is always true regarding the relationship between the one- and two-tailed significance tests? Select all that are true.

Question 10 options:

If the two-tailed test is significant, then the one-tailed test at the same α will also be significant (in the appropriate direction).


If the one-tailed test is significant, then the two-tailed test at the same α will also be significant.


If the two-tailed test is significant, then the one-tailed test at the same α may or may not be significant (in the appropriate direction).


If the one-tailed test is significant, then the two-tailed test at the same α may or may not be significant.

Answer 1

First, lets understand what the problem asks for. If we are using a one-tailed test, the significant Z value is 1.68 while the significant Z value for a two tailed test is 1.95. So a Z statistic is 1.8, we would reject a one tailed test, but not a two tailed. Conversely, if the Z statistic is 2.05, we would reject both the two tailed and the one tailed.

 

Therefore the correct answers are:

 

If the two-tailed test is significant, then the one-tailed test at the same α will also be significant (in the appropriate direction).

 

If the one-tailed test is significant, then the two-tailed test at the same α may or may not be significant.