Question

Consider two independent random samples with the following results:

n1=552       pˆ1=0.67

???n2=462    pˆ2=0.42

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

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.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary confidence interval:

p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	369.84	552	194.04	462	0.25	0.030460076	0.19029935	0.30970065

Hence,

Step - 1: Point estimate = 0.25

Step - 2: Margin of error = (0.30970065 - 0.19029935)/2 = 0.059701

Step - 3: 95% confidence interval:

(0.190, 0.310)