Question

Mr. Bear wishes to do a research on the opinion of Canadians towards Donald Trump. Bersed on prevoon research, he has a pretty good Ideer as to how the result will turn out. How large should the Samples be if the estimate is to produce a positive Opinion between 25 and 29 percent, with a 1% Chance of the estimate being out of the predicted angle: y the .

Answer 1

Confidence level = 1 - 0.01 = 0.99

Confidence interval = (0.25, 0.29)

Margin of error, E = (0.29 - 0.25)/2 = 0.02

Point estimate of proprtion = (0.25 + 0.29)/2 = 0.27

Z value for 99% confidence interval is  2.576

Required sample size to have the interval (0.25, 0.29) with 99% confidence is,

n = (z/E)2 * p(1-p)

= (2.576 / 0.02)2 * 0.27 * (1 - 0.27)

$\approx$ 3270