Bias of the Sample Maximum Estimator
A researcher plans to estimate the maximum value in a population by using the maximum value from a sample. The researcher claims this statistic is an unbiased estimator, assuming the mean of the sampling distribution of the sample maximum equals the population maximum. Which statement best explains the flaw in this claim?
They ignored outlier values, thereby skewing the interpretation of the sample maximum.
They confused the sample maximum with the median of the distribution, leading to an incorrect inference.
They erroneously assumed that the sample maximum is an unbiased estimator of the population maximum, ignoring that it is typically biased and tends to underestimate the true maximum.
They misapplied the formula for variance, leading to an erroneous calculation of the spread around the maximum.
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