A psychologist was interested in whether men tend to show signs of Alzheimer's disease at an earlier age than women. Below are the ages of onset of Alzheimer's symptoms for a sample of men and women. We assume normal data. Men 60 73 70 52 65 51 76 61 68 Women 72 68 57 66 78 67 61 79 64

Here are the summary statistics: Ages of onset Sample size Sample mean Sample SD Men (X) 9 64.00 8.77 Women (Y) 9 68.00 7.31

Define the parameters of interest and state the relevant hypotheses as follows: Let x be the population mean age of onset of Alzheimer's symptoms for men. Let y be the population mean age of onset of Alzheimer's symptoms for women. H0 (the null hypothesis): x - y = 0. H1 (the alternative hypothesis): x - y

A) (3 marks) Test the hypotheses at significance level ? = 5% and include a P-value in your analysis. What is your conclusion? B) (3 marks) If we assume ?x^2 = ?y^2 (the unknown equal variance assumption, where ?x^2 is the true population variance of X), obtain a 95% CI for x - y. What is your conclusion?

Men 60 73 70 52 65 51 76 61 68 Women 72 68 57 66 78 67 61 79 64 Here are the summary statistics: Ages of onset Sample Sample Sample size mean SD Men (X) 9 64.00 8.77 Women (Y) 9 68.00 7.31A B C men women 2 60 72 3 73 68 4 70 57 5 52 66 6 65 78 7 51 67 8 76 61 9 61 79 10 68 64 11 12