Question

Nielson ratings are based on televisions in 5000 households. Nielsen estimates that 15,000 people live in these households. suppose Nielsen reports that American Idol had 55% of the TV audience. interpret this result with a 95% confidence interval, based on a sample of 1500 peoplewhat's the Margin of Error and the Confidence Interval in percentage

Answer 1

The confidence interval is defined as

$I=p\pm z\sqrt[]{\frac{p(1-p)}{n}}$

z = 1.96, n = 1500, and p = 0.55.

$\begin{gathered} I=0.55\pm1.96\cdot\sqrt[]{\frac{0.55(1-0.55)}{1500}} \\ I=0.55\pm0.03 \\ I_1=0.55+0.03=0.58 \\ I_2=0.55-0.03=0.52 \end{gathered}$

Hence, the confidence interval is [0.52,0.58].

Then, we find the margin of error

$\begin{gathered} M=z\cdot\sqrt[2]{\frac{p(1-p)}{n}}=0.96\cdot\sqrt[]{\frac{0.55(1-0.55)}{1500}} \\ M\approx0.03 \end{gathered}$

Therefore, the margin of error is 0.03, approximately.