Question

Which of the following would result in the greatest likelihood of a Type II error (false negative)?

A. ? =.05 and a directional test B. ? =.05 and a non-directional test C. ? =.01 and a directional test D. ? =.01 and a non-directional test

Which of the following would result in the greatest likelihood of a Type I error (false positive)?

A. ? =.05 and a directional test B. ? = .05 and a non-directional test C. ? =.01 and a directional test D. ? =.01 and a non-directional test

Answer 1

The greatest likelihood of a Type II error (false negative): D. ? =.01 and a non-directional test

Reaon: ? is the probability of commiting Type II error.

? decreases --> More difficult to reject Ho --> Power decreases --> ? increases.

Thus, Option A and B should be rejected as ? is greater in both the option.

Two tailed test --> Power decreases --> ? increases

One tailed test --> Power increases --> ? decreases

Thus, for same ? in case of one tailed (Directional) test ? will be smaller so likelihood of Type II error will be smaller. We reject Option C

The greatest likelihood of a Type I error (false positive) is A. ? =.05 and a directional test

Reason: Option C and D can be rejected as in them ? = 0.01 so there is only 1% chance of committing Type I error. Option B is rejected because two-tailed tests (non-directional test) mitigate type I errors (false positives).