The sample variance s² is an unbiased estimator of the population variance $\sigma$² when the denominator of s² is A) n + 1 B) n C) n - 1 D) $$\sqrt { n - 1 }$$

Question

Quizplus · Accepted Answer

The unbiased estimator of the population variance is given by s^2 = (1/n-1) * Σ(xi - x̄)^2, where n is the sample size, xi is the i-th observation, and x̄ is the sample mean. Therefore, the denominator should be (n - 1) to make the estimator unbiased. Choice C corresponds to this denominator, as it includes (n-1) in the denominator. The other choices are incorrect as they either include n in the denominator (A and B) or have a square root term, which is not necessary for an unbiased estimator of the variance (D).

The Sample Variance S2 Is an Unbiased Estimator of the Population

The Sample Variance S² Is an Unbiased Estimator of the Population