Construct the Indicated Confidence Interval for the Difference Between Population $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$

Construct the indicated confidence interval for the difference between population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$ Assume that the samples are independent and that they have been randomly selected.
- $\mathrm { x } _ { 1 } = 37 , \mathrm { n } _ { 1 } = 74$ and $\mathrm { x } _ { 2 } = 50 , \mathrm { n } _ { 2 } = 87 ;$ Construct a $95 \%$ confidence interval for the difference between population proportions $\mathrm { p } _ { 1 } - \mathrm { P } _ { 2 }$ .

A) $0.317 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.683$
B) $- 0.258 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.683$
C) $- 0.229 < p _ { 1 } - p _ { 2 } < 0.079$
D) $0.346 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.654$