Question

Consider two independent random samples with the following results:

n1=562   n2=356

pˆ1=0.17   pˆ2=0.26

Use this data to find the 98% confidence interval for the true difference between the population proportions.

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Step 1 of 3:

Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3:

Find the margin of error. Round your answer to six decimal places.

Step 3 of 3:

Construct the 98% confidence interval. Round your answers to three decimal places.

Answer 1

1)
Here, , n1 = 562 , n2 = 356
p1cap = 0.17 , p2cap = 0.26

point estimate = 0.17 - 0.26 = -0.08

2)
Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.17 * (1-0.17)/562 + 0.26*(1-0.26)/356)
SE = 0.028134

For 0.98 CI, z-value = 2.33

Margin of error = 2.33 * 0.028134 = 0.065552

3)
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.17 - 0.26 - 2.33*0.028134, 0.17 - 0.26 + 2.33*0.028134)
CI = (-0.156 , -0.024)