Construct the Indicated Confidence Interval for the Difference Between the Two

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.
-Two types of flares are tested for their burning times (in minutes) and sample results are given below. $$\begin{array} { l l l } \text { Brand } X & & \text { Brand } Y \\\hline n =35& & \frac { n } { n } = 40 \\\bar { x } = 19.4 & & \bar { x } = 15.1 \\\mathrm {~s} = 1.4 & & \mathrm {~s} = 0.8\end{array}$$
Construct a $95 \%$ confidence interval for the differences $\mu _ { X } - \mu _ { Y }$ based on the sample data.

A) $3.6 < \mu _ { X } - \mu _ { Y } < 5.0$
B) $3.8 < \mu _ { X } - \mu Y < 4.8$
C) $3.5 < \mu X - \mu Y < 5.1$
D) $3.2 < \mu X - \mu Y < 5.4$