Question

The CBS’ television show 60 Minutes has been successful for many years. That show recently had a share of 20, which means that among the TV sets in use at the time the show aired, 20% were tuned to 60 Minutes. Assume that this is based on a sample size of 5000 – which is a typical sample size for this kind of experiments. Construct a 95% confidence interval for the true proportion of TV sets that are tuned to 60 Minutes..

Answer 1

Given:
p = 20% = 0.2, sample proportion
n = 5000, sample size.
Confidence level = 95%

The confidence interval is
(p - 1.96k, p + 1.96k)
where
$k=\sqrt{ \frac{p(1-p)}{n} }=\sqrt{ \frac{0.2*0.8}{5000}} =0.00566$

Therefore the 95% confidence interval is
(0.1943, 0.2057) = (19.4%, 20.6%)

Answer: The 95% confidence interval is (19.4%, 20.6%)