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. Also assume that the population standard deviations are equal ( $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances .
-A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows.
$$\begin{array} { r | r } \text { Type A } & \text { Type B } \\\hline \overline { \mathrm { x } } _ { 1 } = 70.7 \mathrm { hr } & \overline { \mathrm { x } } _ { 2 } = 68.6 \mathrm { hr } \\\mathrm { s } _ { 1 } = 3.8 \mathrm { hr } & \mathrm { s } _ { 2 } = 3.6 \mathrm { hr } \\\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9\end{array}$$
Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type $A$ and the mean drying time for paint type $B$ .

A) $- 1.24$ hrs $< \mu _ { 1 } - \mu _ { 2 } < 5.44$ hours
B) $- 2.16$ hrs $< \mu _ { 1 } - \mu _ { 2 } < 6.36$ hrs
C) $- 2.70 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.90 \mathrm { hrs }$
D) $- 3.47 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.67 \mathrm { hrs }$