Question

Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these households. Suppose Nielsen reports that American Idol had 6565​% of the TV audience. Interpret this result with a​ 95% confidence​ interval, based on a sample size of 12 comma 00012,000 people.

Answer 1

We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%

Explanation:

-From the given information,
`\hat p=0.65`.

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

`CI=\hat p\pm z \sqrt{(\hat p(1-\hat p))/(n)}\\\\\\=0.65\pm 1.96* \sqrt{(0.65* 0.35)/(12000)}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585]`

So, the 95% confidence interval is (0.6515,0.6585).

Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.