Nielsen ratings are based on televisions in 7000 households. Melsen estimates that 17,000 people live in these households. Suppose Nelsen reports that American Idol had 65% of the TV audience.Interpret this result with a 95% confidence interval, based on a sample size of 17 ,000 people. Marginofetror=square % (Round to one decimal place as needed.) Confidence interval is from square % to square %

## Step 1: Calculate the Margin of Error<br />### The margin of error for a 95% confidence interval is calculated using the formula $MarginOfError = 1.96 * \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion (0.65) and $n$ is the sample size (17000). Substituting the values, we get $MarginOfError = 1.96 * \sqrt{\frac{0.65(1-0.65)}{17000}} \approx 0.0071$. Converting this to a percentage, we get $0.0071 * 100 = 0.71\%$.<br /><br />## Step 2: Calculate the Confidence Interval<br />### The confidence interval is calculated as $Sample Proportion \pm Margin Of Error$. In this case, it's $65\% \pm 0.71\%$. This gives us a range from $65 - 0.71 = 64.29\%$ to $65 + 0.71 = 65.71\%$.