Independent Samples from Two Different Populations Yield the Following Data $\bar { x } 1 = 677 , \bar { x } 2 = 211$

Multiple Choice

Independent samples from two different populations yield the following data. $\bar { x } 1 = 677 , \bar { x } 2 = 211$ , $\mathrm { s } _ { 1 } = 30 , \mathrm {~s} _ { 2 } = 30$ . The sample size is 245 for both samples. Find the $80 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$

A) $460 < \mu _ { 1 } - \mu _ { 2 } < 472$
B) $466 < \mu _ { 1 } - \mu _ { 2 } < 466$
C) $463 < \mu _ { 1 } - \mu _ { 2 } < 469$
D) $462 < \mu _ { 1 } - \mu _ { 2 } < 470$