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 thepopulation standard deviations are equal.
-A researcher was interested in comparing the heights of women in two different countries. Independent simple random samples of 9 women from country A and 9 women from country B yielded the following heights (in inches) .
$\begin{array}{c|c}\text { Country A } & \text { Country B } \\\hline 64.1 & 65.3 \\66.4 & 60.2 \\61.7 & 61.7 \\62.0 & 65.8 \\67.3 & 61.0 \\64.9 & 64.6 \\64.7 & 60.0 \\68.0 & 65.4 \\63.6 & 59.0\end{array}$
Construct a $90 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean height of women in country $\mathrm { A }$ and the mean height of women in country B.
(Note: $\bar { x } _ { 1 } = 64.744$ in., $\bar { x } _ { 2 } = 62.556$ in., $s _ { 1 } = 2.192$ in., $\mathrm { s } _ { 2 } = 2.697$ in.)

A) $0.15$ in. $< \mu _ { 1 } - \mu _ { 2 } < 4.23$ in.
B) $0.14$ in. $< \mu _ { 1 } - \mu _ { 2 } < 4.24$ in.
C) $0.17$ in. $< \mu _ { 1 } - \mu _ { 2 } < 4.21$ in.
D) $0.16 \mathrm { in } . < \mu _ { 1 } - \mu _ { 2 } < 4.22 \mathrm { in }$ .