Question

telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Northeast and the South. The representative's belief is based on the results of a survey. The survey included a random sample of 900 northeastern residents and 760 southern residents. 43% of the northeastern residents and 57% of the southern residents reported that they were completely satisfied with their local telephone service. Find the 99% confidence interval for the difference in two 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 99% confidence interval. Round your answers to three decimal places.

Answer 1

Solution

given : n1 900, p10.43, n2 760, p20.57

Step 1 of 3

the critical value for 99% confidence level, za2.576

Step 2 of 3 O

standard error (0) = P1* ( 1- P1) , p2 * (1-p2) n2

0.43(1 0.43) 0.57 (1 0.57) + standard error (op) 900 760

0.43 0.57 0.57 0.43 standard error (op) 760 900

standard error (op)0.024

Step 3 of 3

$\mathbf{formula:}\;\mathbf{Confidence\;Interval:}\;\left (\hat p_1 -\hat p_2 \right )\pm \left ( z_{\frac{\alpha }{2}}*\sigma_{\hat p} \right )$

(0.43 0.57) ± (2.576 0.024)

0.14 0.062

$\mathbf{lower\;endpoint}=-0.14- 0.062=\mathbf{{\color{Red} -0.202}}$

$\mathbf{upper\;endpoint}=-0.14+0.062=\mathbf{{\color{Red} -0.078}}$