Question

From a random sample of 185 children from school G, 108 indicated they wanted to study science in college. From a different random sample of 165 children from school H, 92 indicated they wanted to study science in college. Assuming all conditions for inference are met, which of the following is closest to the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college?A. 1.96 underroot(200/350)(1 − 200/350)/350.B. Underroot(108/185)(1 − 108/185)185 − (92/165)(1−92/165)/165.C. Underroot(108/185)(1 − 108/185)185 + (92/165)(1−92/165)165.D 1.96 underroot(108/185)(1 − 108/185)185 + (92/165)(1 − 92/165)165.E. Underroot(200/300)(1 - 200/300)/350.

Answer 1

C. Underroot(108/185)(1 − 108/185)185 + (92/165)(1−92/165)165.

Explanation:

Sample size, n1 = 185

x1, = 108

P1 = x1 / n1 = 108 / 185 =

Sample size, n2 = 165

x2, = 92

P2 = x2 / n2 = 92/165

Standard Error = sqrt[(p1(1-p1))/n1 + (p2(1-p2))/n2]

sqrt[(108/185(1 - 108/185)) /185 + (92/165(1 - 92/165)) / 165]