(d) A researcher might also be interested in knowing whether the men differ with respect to the intake of other types of food, such as protein or carbohydrates. In the intervention group, the husbands have mean daily carbohydrate intake x1 = 172.5 grams and standard deviation S1 = 68.8 grams. In the control group, the men have mean carbohydrate intake X2 = 185.5 grams and standard deviation $2 = 69.0 grams. Test the null hypothesis that the two populations have the same mean carbohydrate intake. What do you conclude? Question 5: Exercise 12 on page 281 in the textbook. 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 age x2 = 38.8 years and standard deviation S2 = 21.7 years. (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 population means would contain the value 0? Why or why not