Question

Consider two independent random samples with the following results: n1=573 x1=177 n2=604 x2=342 Use this data to find the 95% confidence interval for the true difference between the population proportions. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places. Step 2 of 3: Find the margin of error. Round your answer to six decimal places. Step 3 of 3: Construct the 80% confidence interval. Round your answers to three decimal places.

Answer 1

Solution

Step-1:

p1^=x1/n1=177/573=0.3089005

p2^=x2/n2=342/604=0.5662252

point estimate=p1^-p2^=0.3089005-0.5662252=-0.2573247=-0.257

-0.257

Solution-step-2:

z crit for 80%=1.281552

margin of error=zcrit*sqrt(p1^*(1-p1^)/n1+p26*(1-p2^)/n2)

=1.281552*sqrt(0.3089005*(1-0.3089005)/573+0.5662252*(1-0.5662252)/604)

=.035774

margin of error=.035774

Step 3 of 3: Construct the 80% confidence interval. Round your answers to three decimal places.

point estimate-margin of error,point estimate+margin of error

=-0.257-0.035774,-0.257+0.035774

= -0.292774,-0.221226

=-0.293,-0.221