Answer to Question #167396 in Statistics and Probability for Lali

Question

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?

Answer 1

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.