Construct a 90% Confidence Interval For $\mu _ { 1 } - \mu _ { 2 } .$

Multiple Choice

Construct a 90% confidence interval for $\mu _ { 1 } - \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $$\sigma _ { 1 } ^ { 2 } = \sigma { } _ { 2 } ^ { 2 }$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 10 & \mathrm { n } _ { 2 } = 12 \\\overline { \mathrm { x } } 1 = 25 & \overline { \mathrm { x } } 2 = 23 \\\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9\end{array}$$

A) (0.721, 3.279)
B) (1.335, 3.012)
C) (1.413, 3.124)
D) (1.554, 3.651)