Question

Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this?

Set the value for a Type II error at 0.05.

Set the alpha level at 0.05.

Place the rejection region in both tails.

Both setting the alpha level at 0.05 and placing the rejection region in both tails.

Answer 1

Solution

Back-up Theory

Type I Error is the error of rejecting a null hypothesis when it is true. ................................. (1)

Type II Error is the error of accepting a null hypothesis when it is not true, ........................ (2)

i.e., Alternative is true.

α = P(Type I Error) = probability of rejecting a null hypothesis when it is true .....................(3)

β = P(Type II Error) = probability of accepting a null hypothesis when it is not true, .......... (4)

i.e., Alternative is true.

Significance level α of a test = maximum allowable P(Type I Error) .................................... (5)

Power of a test = 1 – β = probability of rejecting a null hypothesis when it is not true, ........ (6)

Now to work out the solution,

Vide (3) and (5), ‘Set the alpha level at 0.05.’ Answer

‘Set the value for a Type II error at 0.05.’ trivially not the answer since setting Type II error does not affect Type I error.

Choice of one-tail or two-tails depends on the Alternative hypothesis and not on error type. Hence, last two options do not qualify.

DONE