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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

Respuesta :

SOLUTION

We will use the formula

[tex]\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}[/tex]

Plugging in we have

[tex]\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}[/tex]

Hence the answer is

(0.640, 0.680)

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