Respuesta :
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.
Answer:
The correct answer is option (D) (-0.21, 0.01)
Step-by-step explanation:
Solution:
Data Given;
Total number of people in country S = 100
people with blue eyes in country S = 15
Total number of people in country B = 100
People with blue eyes in country B = 25
Let the Y represent number of people with blue eyes in both countries and let Z represent total number of people in both country.
Therefore,
Y₁= 15
Y₂= 25
Z₁ = 100
Z₂ = 100
Sample proportion of country (S₁) = Y1/Z1 = 15/100 = 0.15
Sample proportion of B country (S₂) = Y2/Z2 = 25/100 = 0.25
To calculate the 95% confidence interval, we use the formula;
Confidence interval (CI) =
(S₁ -S₂) ± Zₐ₋₂ * √[S₁( 1-S₁)/z₁ + S₂(1-S₂)/z₂]
At 95% confidence interval, the z-score from standard normal table is 1.96.
Substituting into the formula, we have;
CI = (0.15-0.25) ± 1.96*√[0.15( 1-0.15/100) + 0.25(1-0.25)/100]
= -0.1 ± 1.96*√[(0.15*0.85)/100 + (0.25*0.75)/100]
= -0.1 ± 1.96*√[0.1275/100+ 0.1875/100]
= -0.1 ± 1.96*√[0.001275 + 0.001875]
= -0.1 ± 1.96* √0.00315
= -0.1 ± 1.96*0.0561
= -0.1 +0.11
= -0.1 -0.11 , -0.1 + 0.11
CI = (-0.21, 0.01)
