A study is to be conducted of the percentage of homeowners w

A study is to be conducted of the percentage of homeowners who own at least two television sets. At least how large a sample is required if we wish to be 99% confident that the error in estimating this quantity is less than 0.013? Use a z-score rounded to 2 decimal places.

n =

Solution

We use p=0.5 as estimated.

Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(2.58/0.013)^2*0.5*0.5

=9846.746

Take n=9847