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 the population standard deviations are equal. Independent samples from two different populations yield the following data.
$\bar { x } _ { 1 } = 958 , \bar { x } _ { 2 } = 157 , s _ { 1 } = 77 , s _ { 2 } = 88$
The sample size is 478 for both samples. Find the 85% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$

A) $781 < \mu _ { 1 } - \mu _ { 2 } < 821$
B) $800 < \mu _ { 1 } - \mu _ { 2 } < 802$
C) $794 < \mu _ { 1 } - \mu _ { 2 } < 808$
D) $791 < \mu _ { 1 } - \mu _ { 2 } < 811$