A recent report claimed that Americans are retiring later in life (U.S.News & World Report,August 17,2011).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 .With a = 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

A recent report claimed that Americans are retiring later in life (U.S.News & World Report,August 17,2011).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  .With a = 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

Quizplus · Accepted Answer

The economist should compare the test statistic to the critical value of the t-distribution with n-1 degrees of freedom (in this case, 38-1=37) at the given significance level (a=0.05) to determine if the result is statistically significant. If the test statistic is greater than the critical value (in absolute value), then the economist would reject the null hypothesis and conclude that the mean retirement age has increased.

Using a t-table or a calculator to find the critical value, we get: 
t-critical = ±1.686

Since the test statistic (11eaa4ae_7b0c_e998_9180_bbcdf435e2ae_TB2339_11) is greater than the positive critical value (1.686), we can reject the null hypothesis and conclude that the mean retirement age has increased. Therefore, the answer is A.

A Recent Report Claimed That Americans Are Retiring Later in Life