Question

Current Population Reports presents data on the ages of married people. Ten married couples are randomly selected and have the ages shown here:

Do the data suggest that the mean age of married men is greater than the mean age of married women? Test at 3% level of significance. (You may use R, again, remember to check conditions) (hint: if you look at a problem and are not sure whether you should use paired t-test or 2 sample t-test, you can check whether the data have a linear trend.)

Answer 1

Let ud denotes the difference between mean age of married men and women. To test null hypothesis Ho Md =0.0 against alternative hypothesis H Md > 0.0 Let d denotes the sample mean of difference, Sd denotes the sample standard deviation of difference and n denotes the sample size. Here, d = 3.500, să = 6.7222, sd = 2.5927, n = 10 The test statistic can be written as: vnd -0.0) which under Ho follows at distribution with n - 1 df. We reject Ho at 0.03 level of significance if P-value < 0.03 or if tobs >10.030,11-1 Now, The value of the test statistic = 4.268857 associated degrees of freedom = 9 The critical value = 2.150375 P-value = P(t> 4.268857) = 1 - P(to < 4.268857) = 1 -0.998958 = 0.001042 Since p-value < 0.03 and tabs >I critical = 2.150375, so we reject Ho at 0.03 level of significance Hence, we can conclude that population mean is significantly greater than 0.0