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.
-A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a $99 \%$ confidence interval for $\mathrm { u } _ { 1 }$ - $\mathrm { u } _ { 2 }$ where $u _ { 1 }$ and $u _ { 2 }$ represent the mean for the treatment group and the control group respectively.
$\begin{array} { l } \text { Treatment Group }& \text { Control Group}\\\hline \mathrm{n}_{1}=85 &\mathrm{n}_{2}=75 \\\overline{\mathrm{x}_{1}}=189.1 & \overline{\mathrm{x}_{2}}=203.7 \\\mathrm{~s}_{1}=38.7 & \mathrm{~s}_{2}=39.2\end{array}$

A) $- 1.3 < \mu _ { 1 } - \mu _ { 2 } < 30.5$
B) $- 29.0 < \mu _ { 1 } - \mu _ { 2 } < - 0.2$
C) $- 26.7 < \mu _ { 1 } - \mu _ { 2 } < - 2.5$
D) $- 30.9 < \mu _ { 1 } - \mu _ { 2 } < 1.7$