In: Statistics and Probability
Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 99% confident that their estimate will fall within 1% of the true population proportion?
sample proportion , p̂ =
0.40
sampling error , E = 0.01
Confidence Level , CL= 0.99
alpha = 1-CL = 0.01
Z value = Zα/2 = 2.576 [excel formula
=normsinv(α/2)]
Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (
2.576 / 0.01 ) ² *
0.40 * ( 1 - 0.40 ) =
15923.75
so,Sample Size required=
15924