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Jenkins Vs Hopkins

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I lost 2 points. I chose (c) for the answer as I thought that since both schools took the same percentage size of about 3% of the undergraduates and both had a proportion, p= 0.80, Johns Hopkins and Ohio State would have almost the same sampling variability. I forgot to take into account that each school had different numbers of undergraduates. However, the correct answer is (b). Since a simple random sample of about 3% of Ohio State is about (0.03 x 40,00) = 1,200, it has a larger sample than the (0.03 x 2,000) = 60 undergraduates that make up the simple random sample of about 3% of the undergraduates at Johns Hopkin, meaning Ohio State has smaller variability. Thus, the estimate from Johns Hopkins has more sampling variability than that from Ohio State since it has a smaller sample of 60 undergraduates, making …show more content…

Choice (a) is wrong. The estimate from Johns Hopkins cannot have less sampling variability since it has a smaller sample size (60) compared to Ohio State (1,200); only larger samples give a smaller spread. Choice (c) is untrue since the sample size of Johns Hopkins (60) is not the same size as Ohio State (1,200), so it is not possible for both schools to have the same sampling variability. Choice (d) would be wrong since it is possible to make a statement about the sampling variability of the two estimates, by using the given number of undergraduates and the provided sample sizes which made choice (b) true. Choice (e) would be untrue since as mentioned above, (b) is the correct answer due to the fact that smaller samples give a larger spread and larger samples give a smaller spread, and so the option for none of the answers to be the best

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