Given Information:
Sample size of country S = ns = 100
Sample size of country B = nb = 100
Number of people with blue eyes in country S = 15
Number of people with blue eyes in country B = 25
Confidence level = 95%
Required Information:
Difference in population proportion = ?
Answer:
A (-0.01, 0.21)
Step-by-step explanation:
The difference in mean is
μ = ps - pb
μ = 15/100 - 25/100
μ = 0.15 - 0.25
μ = 0.10
The difference in standard error is
ο = z*√(ps(1 - ps)/ns + pb(1 - pb)/nb)
The z-score corresponding to 95% confidence interval is 1.96
ο = 1.96*√(0.15(1 - 0.15)/100 + 0.25(1 - 0.25)/100)
ο = 1.96*√(0.15(0.85)/100 + 0.25(0.75)/100)
ο = 0.11
Therefore, the difference in population proportion with blue eyes is
μ ± ο
μ + ο, μ - ο
0.10 + 0.11, 0.10 - 0.11
0.21, -0.01
(-0.01, 0.21)
Therefore, the correct option is A.
