Question

Math

Posted 6 months ago

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Silas was curious if sample minimum was an unbiased estimator of population minimum. He started with a large normally distributed population of test scores whose minimum was 51 points.
He then took a random sample of 6 tests and calculated the minimum of the sample. He replaced those tests and repeated this process for a total of 40 trials. His results are summarized in the dotplot below, where each dot represents the minimum score from a sample of 6 tests.
Based on these results, does sample minimum appear to be a biased or unbiased estimator of population minimum?
Hint: The population minimum is 51.
Choose 1 answer:
A Sample minimum appears to be a biased estimator since it consistently underestimated the population minimum.
(B) Sample minimum appears to be a biased estimator since it consistently overestimated the population minimum.
(c) Sample minimum appears to be an unbiased estimator of the population minimum.
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

The population minimum is given as 51 points

step 3

The dot plot shows the distribution of sample minimums from 40 trials

step 4

If the sample minimums frequently fall below the population minimum, the estimator is biased and underestimates the population minimum

step 5

If the sample minimums are symmetrically distributed around the population minimum, the estimator is unbiased

step 6

The cluster of dots around the value of 65 suggests that the sample minimums are consistently above the population minimum of 51

step 7

Since the sample minimums are not symmetrically distributed around the population minimum and are instead consistently higher, the sample minimum is a biased estimator

1 Answer

B

Key Concept

Bias in Estimators

Explanation

An estimator is biased if it consistently overestimates or underestimates the parameter it is estimating. In this case, the sample minimum consistently overestimates the population minimum, indicating bias.

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