Answer to Question #167396 in Statistics and Probability for Lali

Question #167396

A large retailer wants to estimate the proportion of Hispanic customers in a particular state. First, think about how large a sample size (of the retailer’s customers) would be needed to estimate this proportion to within 0.04 accuracy and with 99% confidence. Assume there is no planning value for p* available. IF you decided to go for 0.01 accuracy instead of 0.04 accuracy?


1
Expert's answer
2021-03-01T07:12:16-0500

Given paramters are-

Accuracy x=0.04

At 99% confidence level,

"Z_{\\frac{\\alpha}{2}}=Z_{\\frac{0.99}{2}}=Z_{0.495}=1.875"


error of margin="\\dfrac{x}{2}=\\dfrac{0.04}{2}=0.02"


Let the standard deviation be "\\sigma",

then,

Sample size N="(\\dfrac{Z\\sigma}{E})^2=(\\dfrac{1.875\\sigma}{0.02})^2=(93.75\\sigma)^2=8789\\sigma^2"


If we take the accuracy 0.01 instead of 0.04 then the sample sizee N decreses by 16 times.





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