The latest US Census lists the average household size for all households in the US as 2.61 (i.e. this is μ). The figure below shows possible sampling distributions of X ̄’s for 1000 samples of household sizes. The scale on the horizontal axis is the same in all four cases. a) Assume that two of these sampling distributions show results from 1000 simple random samples, while two others show distributions from a sampling method that is biased. Which two dotplots appear to show samples produced using a biased sampling scheme? Explain your reasoning. Pick one of the distributions that you listed as biased and describe a sample of convenience that might produce this bias. b) For the two sampling distributions that appear to show results from simple random samples, suppose that one comes from 1000 samples of size n = 25 and one comes from 1000 samples of size n = 500. Which distribution goes with which sample size? Briefly explain.
The latest US Census lists the average household size for all households in the US as
2.61 (i.e. this is μ). The figure below shows possible sampling distributions of X ̄’s for
1000 samples of household sizes. The scale on the horizontal axis is the same in all
four cases.
a) Assume that two of these sampling distributions show results from 1000 simple
random samples, while two others show distributions from a sampling method that is
biased. Which two dotplots appear to show samples produced using a biased sampling
scheme? Explain your reasoning. Pick one of the distributions that you listed as biased
and describe a sample of convenience that might produce this bias.
b) For the two sampling distributions that appear to show results from simple random
samples, suppose that one comes from 1000 samples of size n = 25 and one comes from
1000 samples of size n = 500. Which distribution goes with which sample size? Briefly
explain.
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