Question

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

Sample 1	Sample 2
n1 = 400	n2 = 300
p1 = 0.54	p2 = 0.38

(a) What is the point estimate of the difference between the two population proportions?

(b) Develop a 90% confidence interval for the difference between the two population proportions.

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

Answer 1

Given ,

Sample 1 :

Sample size = n1= 400 , Sample proportion = =0.54

Sample 2 :

Sample size = n2= 300 , Sample proportion = =0.38

a ) Point estimate of the difference between the two population proportions is,

b)

We have to find 90% confidence interval for the difference between the two population proportions.

Formula :

Where , is critical value for given confidence level.

Confidence level = 90% = 0.9

Significance level = 1 - = 1 - 0.9 = 0.1 , /2 = 0.05

So critical value is ,  

= = 1.645         { Using Excel ,   =NORMSINV( 1 - 0.05 ) = 1.645 }

The 90% confidence interval for the difference between the two population proportions is ,

The 90% confidence interval for the difference between the two population proportions is ( 0.0983,0.22169)

b)

We have to find 95% confidence interval for the difference between the two population proportions.

Confidence level =95% = 0.95

Significance level = 1 - = 1 - 0.95 = 0.05 , /2 = 0.025

So critical value is ,

= = 1.96        { Using Excel ,   =NORMSINV( 1 - 0.025 ) = 1.96 }

The 95% confidence interval for the difference between the two population proportions is ,

The 95% confidence interval for the difference between the two population proportions is ( 0.0865, 0.2335 )