Which of the following explains why it is easier to reject the null hypothesis w

Question

Which of the following explains why it is easier to reject the null hypothesis with a one-tailed test than with a two-tailed test with all the same parameters?

a. Because the standard deviation in a one-tailed test is larger than that for a two-tailed test

b. Because z-scores are calculated differently in a one-tailed test

c. Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test

d. Because a two-tailed test uses a bimodal distributio

Explanation / Answer

If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction. This means that .025 is in each tail of the distribution of your test statistic. When using a two-tailed test, regardless of the direction of the relationship you hypothesize, you are testing for the possibility of the relationship in both directions.

For one tailed test, If you are using a significance level of .05, a one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest. This means that .05 is in one tail of the distribution of your test statistic. When using a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction.

Hence answer is

c. Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test

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