Question

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

Sample 1	Sample 2
n1 = 500	n2= 200
p1= 0.45	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). 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

solution:-
a.point estimate
=> p1 - p2 = 0.45 - 0.34 = 0.11

b.90% confidence for z is 1.645
confidence interval formula
=> (p1 - p2) +/- z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
=> 0.11 +/- 1.645 * sqrt(0.45(1-0.45)/500 + 0.34(1-0.34)/200)
=> 0.11 +/- 0.0661
=> (0.0439 , 0.1761)

c.95% confidence for z is 1.96
confidence interval formula
=> (p1 - p2) +/- z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
=> 0.11 +/- 1.96 * sqrt(0.45(1-0.45)/500 + 0.34(1-0.34)/200)
=> 0.11 +/- 0.0788
=> (0.0312 , 0.1888)