Television viewers often expre
Television viewers often express doubts about the validity ofcertain commercials. In an attempt to answer their critics, a largeadvertiser wants to estimate the true proportion of consumers whobelieve what is shown in commercials. Preliminary studies indicatethat about 40% of those surveyed believe what is shown incommercials. What is the minimum number of consumers that should besampled by the advertiser to be 99% confident that their estimatewill fall within 1% of the true population proportion?
Answer:
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
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