Question

In a simple random sample of 200 from a population of 2000 colleges, 120 colleges were in favor of a proposal, 57 were opposed, and 23 had no opinion.   Estimate   95% confidence limits for the number of colleges in the population that favored the proposal.

Answer 1

sample success x =		120
sample size          n=		200
sample proportion p̂ =x/n=		0.6000
std error se= √(p*(1-p)/n) =		0.0346
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0679
lower bound=p̂ -E                       =		0.532
Upper bound=p̂ +E                     =		0.668
from above 95% confidence interval for population proportion that favored the proposal =(0.532,0.668)