In a poll of 1000 likely voters 560 say that the United Stat

In a poll of 1000 likely voters, 560 say that the United States spends too little on fighting hunger at home. Find a 98% confidence interval for the true proportion of voters who

Solution

p=560/1000 =0.56

Given a=1-0.98=0.02, Z(0.01) = 2.33 (from standard normal table)

So the lower bound is

p -Z*sqrt(p*(1-p)/n) =0.56 -2.33*sqrt(0.56*(1-0.56)/1000) =0.5234257

So the upper bound is

p +Z*sqrt(p*(1-p)/n) =0.56 +2.33*sqrt(0.56*(1-0.56)/1000) =0.5965743