# Finding the Best Estimator Values of s 2 tend to produce smaller errors by being closer to σ 2 than…

Finding the Best Estimator Values of s2 tend to produce smaller errors by being closer to σ2 than do other unbiased measures of variation. Let’s now consider the biased estimator of (n – 1)s  2/(n + 1). Given the population of values {2, 3, 7}, use the value of σ2 and use the nine different possible samples of size (for sampling with replacement) for the following.a. Find s2 for each of the nine samples, then find the error s2 -σ2 for each sample. Then square those errors. Then find the mean of those squares. The result is the value of the mean square error.b. Find the value of (n – 1)s  2/(n + 1)for each of the nine samples. Then find the error of (n – 1)s  2/(n +1) – σ2 for each sample. Square those errors, then find the mean of those squares. The result is the mean square error.c. The mean square error can be used to measure how close an estimator comes to the population parameter. Which estimator does a better job by producing the smaller mean square error? Is that estimator biased or unbiased?

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