Question

Given two independent random samples with the following results:

n1   463   n2   295
p1   0.77   p2   0.89

Use this data to find the 99%99% 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 99% confidence interval. Round your answers to three decimal places.

Lower Endpoint and Upper Endpoint

Answer 1

n1 = 463, = sample propotion of population 1 = 0.77

n2 = 295, = sample proportion of population 2 = 0.89

Step 1:

Confidene level = c = 0.99

z critical value for (1+c)/2 = (1+0.99)/2 = 0.995

zc = 2.58 (From statistical table of positive z values)

Critical value = 2.58

Step 2 :

Standard error :

(Round to 3 decimal)

Standard error = 0.027

Step 3 :

99% confidence interval is

(Round to 3 decimal)

99% confidence interval is (-0.190, -0.050)

Lower endpoint = -0.190

Upper endpount = -0.050