Question

Consider the following results for independent samples taken from two populations.

Sample 1	Sample 2
n1 = 500	n2= 300
p1= 0.43	p2= 0.36

a. What is the point estimate of the difference between the two population proportions (to 2 decimals)?

b. Develop a 90% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
to

c. Develop a 95% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
to

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

90% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	215	500	108	300	0.07	0.035471115	0.011655208	0.12834479

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	215	500	108	300	0.07	0.035471115	0.00047789217	0.13952211

Hence,

a) Point estimate = 0.07

b) 90% confidence interval:

(0.0117, 0.1283)

c) 95% confidence interval:

(0.0005, 0.1395)