Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-A researcher obtained independent random samples of men from two different towns. She recorded the weights
of the men. The results are summarized below: $$\begin{array} { l l } \frac { \text { Town A } } { \mathrm { n } _ { 1 } = 41 } & \frac { \text { Town B } } { \mathrm { n } _ { 2 } = 21 } \\\overline { \mathrm { x } _ { 1 } } = 165.1 \mathrm { lb } & \overline { \mathrm { x } } _ { 2 } = 159.5 \mathrm { lb } \\\mathrm { s } _ { 1 } = 25.2 \mathrm { lb } & \mathrm { s } _ { 2 } = 25.1 \mathrm { lb }\end{array}$$ Use a 0.05 significance level to test the claim that there is more variation in weights of men from town A than in
weights of men from town B.