Question
The sampling distribution of mean based on a sample of 13 units selected without replacement shows a variance of 5 units. If the population consists of 49 units, estimate the variance of the population
The correct answer is
86.67
For simple random sampling without replacement, using population variance defined with denominator N:
\(\operatorname{Var}(\bar X)=\frac{\sigma^2}{n}\frac{N-n}{N-1}\)
\(5=\frac{\sigma^2}{13}\frac{36}{48}\quad\Rightarrow\quad\sigma^2=5\times13\times\frac{48}{36}=86.67\).
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