Explain why an estimator is or is not unbiased.
Example Problems
A baseball analyst compared three different estimators of the population mean batting average for all 50 players in a league. The true population mean was . Each estimator was simulated using 50 random samples of 6 players.
Estimator A: sample means ranged from to , with the center of the distribution at .
Estimator B: sample means ranged from to , with the center of the distribution at .
Estimator C: sample means ranged from to , with the center of the distribution at .
Based on these results, does Estimator A appear to be a biased or unbiased estimator of population mean batting average?
Estimator A: sample means ranged from to , with the center of the distribution at .
Estimator B: sample means ranged from to , with the center of the distribution at .
Estimator C: sample means ranged from to , with the center of the distribution at .
Based on these results, does Estimator A appear to be a biased or unbiased estimator of population mean batting average?
Ms. Patel was curious if sample range was an unbiased estimator of population range. She recorded the prices of all hoodies at Old Navy and found the population range to be .
She then took a random sample of hoodies and calculated the range of the sample. She replaced those hoodies and repeated this process for a total of trials. Her results are summarized below, where each value represents the sample range from a sample of hoodies.
The sample ranges fell between and . The center of the distribution was at , and most values were below .
Based on these results, does sample range appear to be a biased or unbiased estimator of population range?
She then took a random sample of hoodies and calculated the range of the sample. She replaced those hoodies and repeated this process for a total of trials. Her results are summarized below, where each value represents the sample range from a sample of hoodies.
The sample ranges fell between and . The center of the distribution was at , and most values were below .
Based on these results, does sample range appear to be a biased or unbiased estimator of population range?
A gymnastics coach compared three different estimators of the population mean balance beam score for all gymnasts at a meet. The true population mean was points. Each estimator was simulated using random samples of gymnasts.
Estimator A: sample means ranged from to , with the center of the distribution at .
Estimator B: sample means ranged from to , with the center of the distribution at .
Estimator C: sample means ranged from to , with the center of the distribution at .
Based on these results, does Estimator C appear to be a biased or unbiased estimator of population mean balance beam score?
Estimator A: sample means ranged from to , with the center of the distribution at .
Estimator B: sample means ranged from to , with the center of the distribution at .
Estimator C: sample means ranged from to , with the center of the distribution at .
Based on these results, does Estimator C appear to be a biased or unbiased estimator of population mean balance beam score?
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