A certain town is served by two hospitals. In the larger hospital about 45 babie

Question

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60 percent of the babies born were boys. Which hospital do you think recorded more such days? Most respondents to this question answer that they expect both hospitals to record about the same number of days with over 60 per cent of babies being boys. Explain the error that such respondents are committing.

Explanation / Answer

According to sampling theory the larger hospital is much more likely to report a sex ratio close to 50% on a given day than the smaller hospital. So the correct answer to the question is the smaller hospital.

According to the Law of Large Numbers, with more observations, the experimental average tends to get closer to the true proportion. A big hospital has more observations, so their number will be less likely to stray from 50%, or have less variance.

Also, the variance of the sample proportion is p(1?p)/n, where p is the proability of a boy birth and n is the sample size. Big n (hospital), small variance.

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