Question

Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of adults who retire at age 65 is greater than 62 %. Identify the type I error. Choose the correct answer below. A. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually false. B. Reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 % when it is actually true. C. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62 % when it is actually false. D. Reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually true.

Answer 1

Type I error: D. Reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually true.

Type II error: A. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually false.

Explanation:

A type I error happens when a true null hypothesis is rejected.

A type II error happens when a false null hypothesis is failed to be rejected.

In this case, where the alternative hypothesis is that "the percentage of adults who retire at age 65 is greater than 62%", the null hypothesis will state that this percentage is not significantly greater than 62%.

A type I error would happen when the conclusion is that the percentage is greater than 62%, when in fact it is not.

A type II error would happen when there is no enough evidence to claim that the percentage is greater than 62%, even when the percentage is in fact greater than 62% (but we still don't have evidence to prove it).