Question

Consider two independent random samples with the following results:

n1=585
x1=351
n1=585
x1=351   

n2=730
x2=159
n2=730
x2=159

Use this data to find the 90%90% 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 90%90% confidence interval. Round your answers to three decimal places.

Answer 1

1)

Here, , n1 = 585 , n2 = 730
p1cap = 0.6 , p2cap = 0.218

Point estimate = 0.6 - 0.218 = 0.382

2)

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.6 * (1-0.6)/585 + 0.218*(1-0.218)/730)
SE = 0.0254

For 0.9 CI, z-value = 1.64

margin of error = z *SE
= 1.64 * 0.0254
= 0.041656

3)

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.6 - 0.218 - 1.64*0.0254, 0.6 - 0.218 + 1.64*0.0254)
CI = (0.34 , 0.424)