Question

For a fixed sample size, what happen to the probability of a Type II error if the significance level is decreased from 0.05 to 0.01?

Determine the,

a. rejection region . b. nonrejection region.

c. critical value(s). d. significance value(s).

e. Draw a graph that depicts the answers that you obtain in part(a)-(d).

f. Classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

Short answer

a). It increases because decreasing the significance level is equivalent to shrink the rejection region which results in a expanded non rejection region.

b). For a fixed sample size, the smaller we specify the significance level$\alpha$,the larger will be the probability$\beta$, of not rejecting a false null hypothesis.

Step-by-step solution

Step 1. Explanation

It increases because decreasing the significance level is equivalent to shrink the rejection region which results in a expanded non rejection region.

Step 2. Continue

For a fixed sample size, the smaller we specify the significance level, $\alpha$, the larger will be the probability localid="1651568801871" $\beta$, of not rejecting a false null hypothesis.