The Numbers of Successes and the Sample Sizes Are Given $\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 38 , \mathrm { x } _ { 2 } = 17 , \mathrm { n } _ { 2 } = 38 ; 80 \%$

Multiple Choice

The numbers of successes and the sample sizes are given for independent simple random samples from two populations.Use the two-proportions plus-four z-interval procedure to obtain the specified confidence interval.
- $\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 38 , \mathrm { x } _ { 2 } = 17 , \mathrm { n } _ { 2 } = 38 ; 80 \%$ confidence interval

A) $0.127$ to $0.373$
B) $0.113$ to $0.387$
C) $0.072$ to $0.428$
D) $0.099$ to $0.401$