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.

Question

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.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if the sample minimum is a biased or unbiased estimator of the population minimum, we need to compare the sample minimums to the known population minimum. ‖ ‖ 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.⚹◊What is the formula to calculate the mean and standard deviation of the sample minimum in this scenario?⍭ Generate me a similar question◊

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