Question

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

Sample 1	Sample 2
n1 = 500	n2 = 200
p1 = 0.44	p2 = 0.31

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).  
  to   

Answer 1

a) p1 - p2 = 0.44 - 0.31 = 0.13

b) The pooled sample proportion(P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                                          = (0.44 * 500 + 0.31 * 200)/(500 + 200)

                                                          = 0.403

At 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval for P1 - P2 is

(p1 - p2) +/- z_0.05 * sqrt(P(1 - P)(1/n1 + 1/n2))

= 0.13 +/- 1.645 * sqrt(0.403 * (1 - 0.403) * (1/500 + 1/200))

= 0.13 +/- 0.0675

= 0.0625, 0.1975

c) At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for P1 - P2 is

(p1 - p2) +/- z_0.025 * sqrt(P(1 - P)(1/n1 + 1/n2))

= 0.13 +/- 1.96 * sqrt(0.403 * (1 - 0.403) * (1/500 + 1/200))

= 0.13 +/- 0.0804

= 0.0496, 0.2104