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 simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
-Two types of flares are tested and their burning times are recorded. The summary statistics are given below.

$\begin{array}{ll}\text { Brand } X&\text { Brand } Y\\\mathrm{n}=35 & \mathrm{n}=40 \\\overline{\mathrm{x}}=19.4 \mathrm{~min} & \overline{\mathrm{x}}=15.1 \mathrm{~min} \\\mathrm{~s}=1.4 \mathrm{~min} & \mathrm{~s}=0.8 \mathrm{~min}\end{array}$
Construct a 95\% confidence interval for the differences between the mean burning time of the brand $X$ flare and the mean burning time of the brand $Y$ flare.

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