Question

According to a recent Gallup Poll, 51% (Plus or minus 3%) of Americans support legalizing marijuana. Explain why the 95% confidence interval will be plus or minus 3% when the sample size is 1000 people. How many people do you need to survey in order to have a confidence interval of plus or minus 1%.

Answer 1

Ans:

Point estimate=0.51 or 51%

standard deviation=sqrt(0.51*(1-0.51)/1000)=0.0158

z=1.96 for 95% Confidence level

margin of error=1.96*0.0158=0.03 or 3%

So,95% CI is 51%+/-3%

Now,

margin of error=0.01

sample size required=1.96^2*0.51*(1-0.51)/0.01^2

n=9600