Question: Let \(({{X}_{i}},{{Y}_{i}})\) for i = 1, 2, …,16 where \({{X}_{i}}\) is the height in inches of a young adult female and \({{Y}_{i}}\) is the height in inches of her mother. Suppose that \({{X}_{i}}\) is \(N\left( {{\mu }_{X}},{{\sigma }^{2}} \right)\) and \({{Y}_{i}}\) is \(N\left( {{\mu }_{y}},{{\sigma }^{2}} \right)\), where \({{\sigma }^{2}}=4\) and \(\rho =0.8\) is the correlation coefficient between \({{X}_{i}}\) and \({{Y}_{i}}\), for all \(i=1,2,...,16\).

(a) Let \({{D}_{i}}={{X}_{i}}-{{Y}_{i}}\). What is the mean and the variance of \({{D}_{i}}\) ?

(b) Compute the 95% CI.

(c) Would you reject the null hypothesis?