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.
-Test scores for random samples of students from two different schools were recorded. The summary statistics
are given below. $\begin{array}{lll}\text { School A } & & \text { School B } \\ \mathrm{n}=31 & &{\mathrm{n}}_{=25} \\\bar{x}_{1}=63.7 & & \bar{x}_{2}=59.2 \\\mathrm{~s}_{1}=5.16 & & \mathrm{~s}_{2}=4.89\end{array}$
Use a 0.05 significance level to test the claim that the standard deviation of test scores for students from school A
is different from the standard deviation of test scores for students from school B.