Question

Four different statistics have been proposed as estimators of a population parameter. To investigate The behavior of these estimators, 500 random samples are selected from a known population and it statistic is calculated for each sample. The true value of the population parameter is 75. the graphs below show the distribution of values for each statistic.
A. Which of the statistics appear to be unbiased estimators of the population parameter? How can you tell?

B. Which of the statistics a or B would be better estimate or of the population parameter? Explain your choice.

C. Which of the statistics of your day would be better estimator of the population parameter? Explain your choice.

Answer 1

Based on the information given, the statistics that appear to be unbiased estimators of the population parameter is statistics A.

Solving the statistics.

It should be noted that statistic A is the unbiased estimator of the population parameter. This is because it's centered around the population parameter which is 75.

The statistic that would be a better estimate of the population parameter is statistic A. This is because the sample mean is equal to the population mean which is 75.

The statistic that would be a better estimator of the population parameter is statistic D since it's equal to the population means.

Lastly, it should be noted that statistic C has no distribution shape.

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