Question

5. New Zealand is due for a general election by 2020. Pollsters want to estimate the proportion of the voting population in favor of re‐electing the current Prime Minister, Jacinda Ardern. They want a margin of error of 0.01 and will use a confidence level of 95%.
a. What sample size did they need? (Assume p* = 0.5.) (4 points)
b. The pollsters’ budget was not big enough to accommodate a sample large enough to achieve that narrow margin of error. So, instead, they decided that a margin of error of 0.03 was acceptable. What sample size do they need? (Again, assume p* = 0.5.)

Answer 1

Here z value is 1.96 as P(-1.96<z<1.96)=0.95

a. Here Margin of Error is 0.01 and p=0.5

So we will find n using formula of E

$E=z*\sqrt{\frac{pq}{n}}$

So $n=(\frac{z}{E})^2*p*q=(\frac{1.96}{0.01})^2*0.5*0.5=9604$

b. Now E=0.03

So $n=(\frac{z}{E})^2*p*q=(\frac{1.96}{0.03})^2*0.5*0.5=1067.1=1068$