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.
-Random samples of 13 women and 11 men yielded the following scores on a test: Women: $\quad 70,78,62,96,75,68,41,74,80,47,73,94,65$
Men: $\quad 72,60,52,87,66,74,95,50,81,70,72$ Use a 0.05 significance level to test the claim that test scores for women have a larger standard deviation than
test scores for men. $$\left( \text { Note: } \mathrm { s } _ { 1 } = 15.588 \text { and } \mathrm { s } _ { 2 } = 13.754 \right) \text {. }$$