Question

Given two independent random samples with the following results:

n1   297   n2   93
p1   0.67   p2   0.41

Use this data to find the 98% confidence interval for the true difference between the population proportions.

Step 1 of 3:

Find the critical value that should be used in constructing the confidence interval.

Step 2 of 3:

Find the value of the standard error. Round your answer to three decimal places.

Step 3 of 3:

Construct the 98% confidence interval. Round your answers to three decimal places.

Answer 1

Critical value = $Z_{\alpha /2} = Z_{ 0.02 /2 } = 2.33$

Standard Error =

/((P1 * q1)/n 1) + ((P2 * q2)/n2) 0.0578

$(\hat{P1} - \hat{P2}) \pm Z_{\alpha/2} * \sqrt{((\hat{P1} *\hat{ q1} )/ n1) + ((\hat{P2} * \hat{q2} )/ n2)}$
$Z_{\alpha /2} = Z_{ 0.02 /2 } = 2.33$
Lower Limit =
(0.67-0.41)-Z0.02/2 * V ((0.67 * 0.33)/297) + ((0.41 * 0.59) /93) 0.1254

Upper Limit =
(0.67-0.41)+Zo.02/2*((0.67 0.33)/297) +((0.41 0.59)/93) 0.3946

98% Confidence interval is ( 0.125 , 0.395 )
( 0.125 < ( P1 - P2 ) < 0.395 )