Question

Suppose you are running a presidential campaign for my dog Jasper. Nobody has ever done polling for a dog before. I have asked you to poll the population to see if Jasper can beat the other candidate in the election. Explain how you would do this to ensure a margin of error of 5%

Answer 1

1. Let p is estimate proportion, then

        Z_0.05/2*(p*(1-p)/n)^1/2 = 0.05 => 1.96*(p*(1-p)/n)^1/2 = 0.05

• n = p*(1-p)/(0.05/1.96)² = 1536.64 *p*(1-p)

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =1537*1/4 =384.25

So if no estimate were available for the proportionwe need 385 sample size.

Remember the margin of error is given as

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

we simply need to solve for n