Question

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 1

we have:

p = 0.75

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

`\begin{gathered} CI=p\pm z\sqrt[]{(p(1-p))/(n)} \\ CI=0.75\pm1.96*\sqrt[]{(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}`

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

margin of error is 0.75 x 100 = 75%