Television viewers often express doubts about the validity of certain commercials. In an attempt to answer...

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?

Expert Solution

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

orchestra answered 3 years ago

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