Researcher A broadcasts a TV poll to all of Portland, which produces a sample of

Question

Researcher A broadcasts a TV poll to all of Portland, which produces a sample of 650 Portlanders (230 males, 420 females). Researcher B conducts a random sample of size 200 from all of Portland.

a) Researcher B claims that their sample of 200, although smaller than the 650, would likely better reflect Portland opinion than the larger sample. Is the Researcher correct? If so, give two convincing reasons in support of this claim. If not, explain why not.

b) Later, from the larger sample of 650: A combined smaller sample of 130 was made by combining a random 84 of the 420 females, a random 46 of the 230 males (thus each of the 650 respondents had an equal 1 in 5 chance of being included in the sample of 130). Is this resulting sample of 130 a Simple Random Sample (SRS) from the 650? Explain why or why not. If your answer is no, prove it by describing a specific sample of 130 (stating the male/female counts) that could not be selected from the 650, using the described method.

Explanation / Answer

(a)

The claim of researcher B is true, because although B has a smaller sample size, its sample is unbiased, and while A has a larger sample size, its sample is biased. This is because A draws its sample only from those people who watched TV, while there are many people who don't have a TV and so their opinion is not considered in A's sample, which produces a bias.

(b)

NO, this is not a SRS of the 650 size sample, This is because using the method described above, the ratio of total count of men and women would always be same and equal to 1.8

This excludes the samples for which this ratio is significantly less than 1.8, or significantly greater than 1.8

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