Construct a 95% Confidence Interval For $\mu _ { 1 } - \mu _ { 2 }$

Multiple Choice

Construct a 95% 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 $\sigma \underset { 1 } { 2 } = \sigma _{ 2 } ^{ 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 7 \\\overline { \mathrm { x } } 1 = 4.1 & \overline { \mathrm { x } } 2 = 5.5 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 2.51\end{array}$$

A) (-3.406, 0.606)
B) (-1.132, 1.543)
C) (-1.679, 1.987)
D) (2.112, 2.113)