Question

Please help with these two questions?

Question #1:

Consider the following results for independent samples taken from two populations. Sample 1 Sample 2 ni = 400 n2 = 200 P1 = 0.45 P2 = 0.31 a. What is the point estimate of the difference between the two population proportions (to 2 decimals)? 0.12 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 ®

Question #2:

Answer 1

b)

Here, , n1 = 400 , n2 = 200
p1cap = 0.45 , p2cap = 0.31

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.45 * (1-0.45)/400 + 0.31*(1-0.31)/200)
SE = 0.0411

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.45 - 0.31 - 1.64*0.0411, 0.45 - 0.31 + 1.64*0.0411)
CI = (0.0726 , 0.2074)

c)

Here, , n1 = 400 , n2 = 200
p1cap = 0.45 , p2cap = 0.31

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.45 * (1-0.45)/400 + 0.31*(1-0.31)/200)
SE = 0.0411

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.45 - 0.31 - 1.96*0.0411, 0.45 - 0.31 + 1.96*0.0411)
CI = (0.0594 , 0.2206)

2)

a)

difference = 13.1 - 11.5 = 1.6

b)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(6.25/40 + 9/30)
sp = 0.6755

Given CI level is 0.9, hence α = 1 - 0.9 = 0.1                  
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.645                  
                  
Margin of Error                  
ME = tc * sp                  
ME = 1.645 * 0.6755                  
ME = 1.111                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (13.1 - 11.5 - 1.645 * 0.6755 , 13.1 - 11.5 - 1.645 * 0.6755                  
CI = (0.49 , 2.71)                  

c)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(6.25/40 + 9/30)
sp = 0.6755

Given CI level is 0.95, hence α = 1 - 0.95 = 0.05                  
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.96                  
                  
Margin of Error                  
ME = tc * sp                  
ME = 1.96 * 0.6755                  
ME = 1.324                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (13.1 - 11.5 - 1.96 * 0.6755 , 13.1 - 11.5 - 1.96 * 0.6755                  
CI = (0.28 , 2.92)