Exercise · ZW-ESTIMATOR-005 · ★☆☆ Basic
For the data \(2,\ 4,\ 6,\ 8\), what is the sample variance \(S^2\) (dividing by \(n-1\))?
Choose one option.
Show answer
- C. \(\tfrac{20}{3}\)
Explanation
The mean is \(5\) and the sum of squared deviations is \(9+1+1+9=20\); \(S^2=20/3\). Dividing by \(n=4\) would give \(5\), which is biased downward.
Review the concept: Estimator
An estimator \(\hat\theta\) is a rule \(T\), a function of the random sample \(X_i\), that produces a value used to approximate an unknown population parameter \(\theta\).
\[\hat\theta=T(X_1,\dots,X_n)\]
More practice problems: estimator
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- ZW-ESTIMATOR-007 A population has σ^2=36. With n=9, what is the variance of bar X?
- ZW-ESTIMATOR-008 With n=25, which unbiased estimator of μ is preferable: bar X or just X_1?
- ZW-ESTIMATOR-009 If μ=3 and hatμ=2bar X is used, what is the bias?