Question

17. If you want a poll to have a margin of error of 3.25%, how large will your sample have to be? Round your answer to the nearest whole number. people

Answer 1

We have to calculate the sample size in order for the margin of error to be 3.25% or less. We assume we are doing a poll for a proportion with a confidence level of 95%.

We have a formula that relates margin of error M and sample size n for a 95% confidence level:

$M=\frac{1}{\sqrt[]{n}}$

NOTE: M is expressed in decimal form, not percentage.

As we know that M=0.0325, we can calculate n as:

$\begin{gathered} M=0.0325=\frac{1}{\sqrt[]{n}} \\ \sqrt[]{n}=\frac{1}{0.0325} \\ n=(\frac{1}{0.0325})^2 \\ n\approx(30.77)^2 \\ n\approx946.74 \\ n=947 \end{gathered}$

Answer: the minimum sample size is 947 people.