Fund the Critical Value Margin of Error and the Confidence I

Fund the Critical Value, Margin of Error and the Confidence Interval for estimating the population proportion p.

Confidence Interval: p^

Solution

p=200/500=0.4

Given a=1-0.9=0.1, the critical value is Z(0.05) = 1.645 (from standard normal table)

The Margin of Error is Z*sqrt(p*(1-p)/n)

=1.645*sqrt(0.4*0.6/500) =0.03604014

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.4 -0.03604014 =0.3639599

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.4 +0.03604014 =0.4360401