Question

Consider two independent random samples with the following results:

n1=195 x1=35    n2=408 x2=352

Use this data to find the 90% confidence interval for the true difference between the population proportions.

Step 2 of 3:

1-find the point estimate

2-Find the margin of error. Round your answer to six decimal places.

3-Construct the 90% confidence interval. Round your answers to three decimal places.

Answer 1

Point estimate = (p̂1 - p̂2) = ( 0.1795 - 0.8652 ) = - 0.686

Margin of Error = Z(0.1/2) * √(((\hat{P1} *\hat{ q1} )/ n1) + ((\hat{P2} * \hat{q2} )/ n2)) = 0.053078

(p̂1 - p̂2) ± Z(α/2) * √( ((p̂1 * q̂1)/ n1) + ((p̂2 * q̂2)/ n2) )
Z(α/2) = Z(0.1 /2) = 1.645
Lower Limit = ( 0.1795 - 0.8652 )- Z(0.1/2) * √(((0.1795 * 0.8205 )/ 195 ) + ((0.8652 * 0.1348 )/ 408 ) = -0.739
upper Limit = ( 0.1795 - 0.8652 )+ Z(0.1/2) * √(((0.1795 * 0.8205 )/ 195 ) + ((0.8652 * 0.1348 )/ 408 )) = -0.633
90% Confidence interval is ( -0.739 , -0.633 )
( -0.739 < ( P1 - P2 ) < -0.633 )