Question

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

Sample 1 Sample 2

n1 = 500 n2= 300

p1= 0.49 p2= 0.34

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).
to

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

Answer 1

a) The point estimate for the difference between the two population proportions is computed here as:

p₁ - p₂ = 0.49 - 0.34 = 0.15

Therefore 0.15 is the required point estimate here.

b) From standard normal tables, we have here:
P( -1.645 < Z < 1.645) = 0.9

The pooled proportion here is computed as :

Therefore, now the standard error here is computed as:

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval for the difference in the 2 proportions.

c) From standard normal tables, we have:
P( -1.96 < Z < 1.96) = 0.95

Therefore the 95% confidence interval here is computed as:

This is the required 95% confidence interval for the difference in 2 proportions here.