Question

Consider two independent random samples with the following results:

n1=173 x1=146   n2=58 x2=30

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 95% confidence interval. Round your answers to three decimal places. (upper and lower endpoints)

Answer 1

Here, , n1 = 173 , n2 = 58
p1cap = 0.844 , p2cap = 0.517

1)
Point estimate = p1 - p2
= 0.844 - 0.517
= 0.327

2)

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.844 * (1-0.844)/173 + 0.517*(1-0.517)/58)
SE = 0.0712

For 0.95 CI, z-value = 1.96

Margin of error = z *SE
= 1.96 * 0.0712
= 0.1395128

3)

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.844 - 0.517 - 1.96*0.0712, 0.844 - 0.517 + 1.96*0.0712)
CI = (0.187 , 0.467)