It is believed that 25 of US homes have a direct satellite t

It is believed that 25% of U.S. homes have a direct satellite television receiver. Round your answers up to a whole number if necessary for the following questions. How a large a sample is necessary to estimate the true population of homes that have a direct satellite television receiver with 99% confidence and within 4 percentage points? How large a sample is necessary if nothing is known about the population?

Solution

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.58
Samle Proportion = 0.25
ME = 0.04
n = ( 2.58 / 0.04 )^2 * 0.25*0.75
= 780.0469 ~ 781