A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t₃₇ = 1.92. With α = 0.05, she ________. A) rejects the null hypothesis and concludes that the mean retirement age has increased B) rejects the null hypothesis and concludes that the mean retirement age has not increased C) does not reject the null hypothesis and does not conclude that the mean retirement age has changed D) does not reject the null hypothesis and does not conclude that the mean retirement age has increased

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean retirement age is 62, and the alternative hypothesis is that the mean retirement age has increased. The economist is conducting a one-sample t-test with a sample size of 38 and α = 0.05.

Using a t-distribution table with 37 degrees of freedom (n-1), the critical value for a two-tailed test at α = 0.05 is 2.024. Since the calculated t-statistic of 1.92 is less than the critical value, the economist fails to reject the null hypothesis.

Therefore, she cannot conclude that the mean retirement age has increased. However, given the test's limitations, she may want to consider conducting further research.

A Recent Report Claimed That Americans Are Retiring Later in Life