Question

Given two independent random samples with the following results: 

n1=170x1=36    

n2=123x2=65 

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

Step 1 of 4 : Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 2 of 4: Find the margin of error. Round your answer to six decimal places.

Step 3 of 4: Construct the 90% confidence interval. Round your answers to three decimal places.

Answer 1

1)
p1cap = X1/N1 = 36/170 = 0.212
p2cap = X2/N2 = 65/123 = 0.528

2)

Here, , n1 = 170 , n2 = 123
p1cap = 0.212 , p2cap = 0.528

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.212 * (1-0.212)/170 + 0.528*(1-0.528)/123)
SE = 0.0549
For 0.9 CI, z-value = 1.64

margin of error = 1.64 * 0.0549
= 0.090036

3)

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.212 - 0.528 - 1.64*0.0549, 0.212 - 0.528 + 1.64*0.0549)
CI = (-0.406 , -0.226)