A member of state legislature wants to determine what fracti

A member of state legislature wants to determine what fraction of the voters in his district favors a proposal refunding excess state sales tax revenue to the tax payers. A random sample of 150 voters in his district shows 80 in favor. Let p be the population proportion in favor of proposal.

What is the margin of error (E) for this estimate with 95% confidence?

Solution

p=80/150 = 0.5333333

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the margin of error is

Z*sqrt(p*(1-p)/n)

=1.96*sqrt(p*(1-p)/n)

=1.96*sqrt(0.5333333*(1-0.5333333)/150)

=0.07983865