[AP Statistics] 7.1b Biased and Unbiased Estimators - Oliver Khamky | Laabri

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Mrs. Chauvet has an interesting approach to assigning grades in her statistics class. Of the 5 tests students take throughout the semester, Mrs. Chauvet selects a random sample of 3, finds the average score of these tests, and records this average as the student’s final grade. Joe’s test scores are as follows: 93, 87, 96, 78, 90.
Is the sample mean an unbiased estimator of the population mean? How do you know?

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Is the sample range an unbiased estimator of the population range? How do you know?

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Compared to the other statistics, how would you describe Statistic A?

High Bias and High Variability

High Bias and Low Variability

Low Bias and High Variability

Low Bias and Low Variability

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Compared to the other statistics, how would you describe Statistic B?

High Bias and High Variability

High Bias and Low Variability

Low Bias and High Variability

Low Bias and Low Variability

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Compared to the other statistics, how would you describe Statistic C?

High Bias and High Variability

High Bias and Low Variability

Low Bias and High Variability

Low Bias and Low Variability

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Is sample proportion an unbiased estimator of the population proportion?

Yes

No

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Explain.

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How does the variability of this sampling distribution compare with the variability of the sampling distribution from the previous problem?

Less variability than the previous problem

More variability than the previous problem

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What does this indicate about increasing the sample size?

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i

ii

iii

iv

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Explain

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i

ii

iii

iv

1

Explain

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Are there any problems above that you would like to go over in class? Indicate the question numbers below (Numbers refer to the Formative question number). I'll try to cover anything that is highly requested.