Discussion
Which of the following is NOT true for stratified random sampling ?
A larger sample would be required from a stratum if :
Answer: C
The statement that is NOT true is that a larger sample is needed when the sampling cost per unit is large in the stratum.
Under optimum allocation the sample size in stratum h is
\[ n_{h} \propto \frac{N_{h} S_{h}}{\sqrt{c_{h}}} \]
It grows with the stratum size \(N_{h}\) and the stratum variability \(S_{h}\), and falls as the cost per unit \(c_{h}\) rises. So a costly stratum gets a smaller sample, not a larger one.
Options A, B and D (large size, large variability, low cost) all correctly call for a larger sample.
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