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 and that they have been randomly selected.
-Independent samples from two different populations yield the following data. $\overline { x _ { 1 } } = 383 , \overline { x _ { 2 } } = 448$ , s1 $= 44$ , s2 $= 18$ . The sample size is 177 for both samples. Find the 85 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

A) $- 72 < \mu _ { 1 } - \mu _ { 2 } < - 58$
B) $- 66 < \mu _ { 1 } - \mu _ { 2 } < - 64$
C) $- 79 < \mu _ { 1 } - \mu _ { 2 } < - 51$
D) $- 71 < \mu _ { 1 } - \mu _ { 2 } < - 59$