Suppose that you wish to compare the characteristics of tuberculosis meningitis in patients infected with HIV ...

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 X 1 = 27.9 years and standard deviation S​1 =  5.6 years: a sample of 19 who are not infected has mean age X2= 38.8 years and standard deviation 21.7 years.  Assume unequal variances: 

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

b) Do you expect that 95% confidence interval for the true difference in population means would contain the value 0? why or why not?