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.
-$\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 60 , \mathrm { x } _ { 2 } = 29 , \mathrm { n } _ { 2 } = 77 ; 95 \%$ confidence interval
A)$0.288$ to $0.615$
B) $- 0.122$ to $0.646$
C) $- 0.092$ to $0.236$
D) $0.258$ to $0.646$

Question

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.
-$\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 60 , \mathrm { x } _ { 2 } = 29 , \mathrm { n } _ { 2 } = 77 ; 95 \%$ confidence interval  
A)$0.288$ to $0.615$
B) $- 0.122$ to $0.646$
C) $- 0.092$ to $0.236$
D) $0.258$ to $0.646$

Quizplus · Accepted Answer

The two-proportions plus-four z-interval procedure adjusts the sample sizes and successes by adding 1 to each success and 2 to each sample size, then calculates the confidence interval. This results in the interval $-0.092$ to $0.236$.

The Numbers of Successes and the Sample Sizes Are Given x1=27,n1=60,x2=29,n2=77;95%\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 60 , \mathrm { x } _ { 2 } = 29 , \mathrm { n } _ { 2 } = 77 ; 95 \%x1​=27,n1​=60,x2​=29,n2​=77;95%

The Numbers of Successes and the Sample Sizes Are Given $\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 60 , \mathrm { x } _ { 2 } = 29 , \mathrm { n } _ { 2 } = 77 ; 95 \%$