Question

choose the correct answer below

oa. decreasing a increases the probability of rejecting the null hypothesis, which
rejecting the null hypothesis when it is true, a type ii error.

ob. decreasing a increases the probability of rejecting the null hypothesis. this
the complement, failing to reject the null hypothesis, which could increase th
alternative hypothesis when it is false, a type ii error.

oc. decreasing a decreases the probability of failing to reject the null hypothesi
the complement, rejecting the null hypothesis, which could increase the pro
hypothesis when it is true, a type ii error.

od. decreasing a decreases the probability of rejecting the null hypothesis. thi
the complement, not rejecting the null hypothesis, which could increase the
null hypothesis when it is false, a type ii error.

Explanation:

In hypothesis testing, $\alpha$ (significance level) is the probability of rejecting the null hypothesis when it is true (Type I error). Decreasing $\alpha$ means we are less likely to reject the null hypothesis. The complement of rejecting the null hypothesis is not rejecting the null hypothesis. If we decrease the probability of rejecting the null hypothesis (lower $\alpha$), we could increase the probability of not rejecting the null hypothesis when it is false (Type II error).

Answer:

D. Decreasing $\alpha$ decreases the probability of rejecting the null hypothesis. This the complement, not rejecting the null hypothesis, which could increase the null hypothesis when it is false, a type II error.