Determine The $95 \%$ Confidence Interval of the True Difference in the Means

Multiple Choice

Determine the $95 \%$ confidence interval of the true difference in the means. A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Use $\alpha =$$0.05$ .
$\begin{array}{|l|l|l|}\hline & \text { Africa } & \text { Asia } \\\hline \overline{\bar{X}} & 55.3 & 65.2 \\\hline \sigma & 8.1 & 9.3 \\\hline n & 53 & 42 \\\hline\end{array}$

A) $- 12.16 < \mu _ { 1 } - \mu _ { 2 } < - 686$
B) $- 13.46 < \mu _ { 1 } - \mu _ { 2 } < - 6.34$
C) $- 11.35 < \mu _ { 1 } - \mu _ { 2 } < - 7.58$
D) $- 16.33 < \mu _ { 1 } - \mu _ { 2 } < - 5.98$