Question

identify the type i error and the type ii error that correspond to the given hypothesis.
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 greater than 62% when the percentage is actually equal to 62%.
b. fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually greater than 62%.
c. reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62% when that percentage is actually greater than 62%.
d. reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when the percentage is actually equal to 62%.
identify the type ii error. choose the correct answer below.
a. reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62% when that percentage is actually greater than 62%.
b. fail to reject the null hypothesis that the percentage of adults who retire at age 65 is greater than 62% when the percentage is actually equal to 62%.
c. reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when the percentage is actually equal to 62%.
d. fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually greater than 62%.

Explanation:

• Type I error: A Type I error occurs when we reject the null hypothesis (\(H_0\)) when it is actually true. The null hypothesis \(H_0:p = 0.62\) (where \(p\) is the proportion of adults who retire at age 65). Rejecting \(H_0\) when \(p = 0.62\) (i.e., the null hypothesis is true) is a Type I error.
• Type II error: A Type II error occurs when we fail to reject the null hypothesis (\(H_0\)) when it is actually false. The alternative hypothesis \(H_1:p>0.62\). Failing to reject \(H_0\) (\(p = 0.62\)) when \(p>0.62\) (i.e., the null hypothesis is false) is a Type II error.

Answer:

• Type I error: D. Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually equal to 62%.
• Type II error: D. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually greater than 62%.