Question

A group of 5,000 employees is being asked to choose whether or not to join a union. In a sample of 100 employees, 63 indicate they will vote in favor of the union. Create a 99% confidence interval for the population proportion. If they need over 55% of the votes to be in favor in order to form a union, can you say with 99% confidence that it will pass? (3 points)

Answer 1

sample success x =		63
sample size          n=		100
sample proportion p̂ =x/n=		0.6300
std error se= √(p*(1-p)/n) =		0.0483
for 99 % CI value of z=		2.576
margin of error E=z*std error   =		0.1244
lower bound=p̂ -E                       =		0.5056
Upper bound=p̂ +E                     =		0.7544

from above:

99% confidence interval for the population proportion =( 0.506 , 0.754)

since confidence interval contains values below 0.55 ( 55%) , therefore we can not conclude with 99% confidence that  it will pass.