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

We will use the formula

`\begin{gathered} p\pm_Z\sqrt{(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{(0.66(1-0.66))/(590)} \\ 0.66\pm\sqrt{(0.66*0.34)/(590)} \\ 0.66\pm0.0195022 \\ 0.67950,0.6404978 \end{gathered}`

Hence the answer is

(0.640, 0.680)