Suppose that you wish to compare the characteristics of tuberculosis meningitis in patients infected with HIV and those who are not infected. In particular, you would like to determine whether the two populations have the same mean age. A sample of 37 infected patients has mean age x1 = 27.9 years and standard deviation s1 = 5.6 years; a sample of 19 patients who are not infected has mean agex2 = 38.8 years and standard deviation s2 = 21.7 years [17].

(a)Test the null hypothesis that the two populations of patients have the same mean age at the 0.05 level of significance.

(b)Do you expect that a 95% confidence interval for the true difference in popu- lation means would contain the value 0? Why or why not?