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another way to look at this could be to compare a study done on a particular medicine, when study is on a small group of participants versus a large group the results must be shown as proportional and can only be relevant as they are calculated as how many are made well to how many do not receive any favorable results. Many times when a study is done on the effects of a substance on another it must be shown that the margin of error is proportionate to the study. As for instance the drug which conquered polio was simply a vaccine made of the polio virus and had great affects on the disease. Although there was a margin of error that the US government felt was acceptable to allow the drug to be forcibly injected in all children of the late 50's.

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Q: How does the standard deviation impact the margin of error?
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