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Nielson ratings are based on televisions in 5000 households. Nielsen estimates that 12,000 people live in these households. suppose Nielsen reports that American Idol had 75% of the TV audience. interpret this result with a 95% confidence interval, based on a sample of 12000 peoplewhat's the Margin of Error and the Confidence Interval in percentage

Answer :

we have:

p = 0.75

We calculate the confidence interval using this value at 95% confidence level:

[tex]\begin{gathered} CI=p\pm z\sqrt[]{\frac{p(1-p)}{n}} \\ CI=0.75\pm1.96\times\sqrt[]{\frac{0.75(1-0.75)}{12000}} \\ CI=0.75\pm0.0077 \\ CI=\text{0.75+0.0077=0.7577} \\ or \\ CI=0.75-0.0077=0.7423 \end{gathered}[/tex]

So, the 95% confidence interval is 74.23% and 75.77%

margin of error is 0.75 x 100 = 75%

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