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.
-Two types of flares are tested and their burning times are recorded. The summary statistics are given below.
Use a 0.05 significance level to test the claim that the burning times for Brand X flares have the same variance as
the burning times for Brand Y flares. $$\begin{array}{l}\frac { \text { Brand } X } { n = 35 } \quad \frac { \text { Brand } Y } { n = 41 }\\\bar { x } = 19.4 \mathrm {~min} \quad \bar { x } = 15.1 \mathrm {~min}\\\mathrm { s } = 1.4 \mathrm {~min} \quad \mathrm {~s} = 0.8 \mathrm {~min}\end{array}$$