Answer to Question #100086 in Statistics and Probability for Juliet Beglaryan

Question

The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-year-olds. Of these 1048 teenagers, 692 had a television in their room.
What is the number of teenagers needed for 90% confidence interval within 0.02 of the true proportion.

Answer 1

The number of teenagers needed:

$$n=\left(\frac{z^*}{E}\right)^2p(1-p)$$

$z^*=1.645$ for 90% confidence level.

$$n=\left(\frac{1.645}{0.02}\right)^2\left(\frac{692}{1048}\right)\left(1-\frac{692}{1048}\right)=1517.4$$

We round up to 1518.