Suppose two statistics, A and B, exist to estimate the same population parameter (theta). (Note that

Suppose two statistics, A and B, exist to estimate the same population parameter θ (theta). (Note that θ could be any parameter: μ, σ², σ, etc.) Suppose the two statistics have sampling distributions as shown in Figure 5.6. On the basis of these sampling distributions, which statistic is more attractive as an estimator of θ?

Figure 5.6

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f(A) 0 a. Unbiased sample statistic for the parameter 0 A f(B) 0 Bias Mean of sampling distribution b. Biased sample statistic for the parameter 8 B