Question

In a recent poll 590 people were asked if they liked dogs, and 66% said they did. Find the margin of error of this poll at the 90% confidence level. Give your answer to three decimals

Answer 1

SOLUTION

We will use the formula

$\begin{gathered} p\pm_Z\sqrt{\frac{p(1-p)}{n}} \\ where\text{ p = 66\% = 0.66} \\ n=590 \\ Z_{90\%}=1.645 \end{gathered}$

Plugging in we have

$\begin{gathered} 0.66\pm_1.645\sqrt{\frac{0.66(1-0.66)}{590}} \\ 0.66\pm\sqrt{\frac{0.66\times0.34}{590}} \\ 0.66\pm0.0195022 \\ 0.67950,0.6404978 \end{gathered}$

Hence the answer is

(0.640, 0.680)