Question

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

Sample 1	Sample 2
n1 = 400	n2= 300
p1= 0.49	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.

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

Answer 1

Given that,

For sample 1 : n1 = 400 and p1-bar = 0.49

For sample 2 : n2 = 300 and p2-bar = 0.36

a) The point estimate of the difference between the two population proportions is, (0.49 - 0.36) = 0.13

b) A 90% confidence level has significance level of 0.10 and critical value is,

The 90% confidence interval for (p1 - p2) is,

Therefore, 90% confidence interval for the difference between the two population proportions is (0.0686, 0.1914)

c) A 95% confidence level has significance level of 0.05 and critical value is,

​​​​

Therefore, a 95% confidence interval for the difference between the two population proportions is (0.0569, 0.2031)