Question

18. If you want a poll to have a margin of error of 3.33%, how large will your sample have to be? Round your answer to the nearest whole number.people

Answer 1

ANSWER:

902 people

STEP-BY-STEP EXPLANATION:

We have that the margin of error is given by the following formula:

$e=\frac{1}{\sqrt[]{n}}\cdot100\text{\%}$

We know the value of the error, therefore we can replace and calculate the sample size:

$\begin{gathered} 3.33\text{\%}=\frac{1}{\sqrt[]{n}}\cdot100\text{\%} \\ \frac{1}{\sqrt[]{n}}=0.0333 \\ \sqrt[]{n}=\frac{1}{0.0333} \\ n=\mleft(\frac{1}{0.0333}\mright)^2 \\ n=901.8\cong902 \end{gathered}$

The sample size will be 902 people