Quality Quiz from Professor Cleary
"B" is correct.
To understand why Quinn should be quarantined for his curious conclusion, one must understand the binomial central limit theorem, which explains how the sampling distribution of proportions behaves.
With a known population of 10,000 residents of Quincy, one would need to collect many samples of the size 100—not simply one group of 100. With multiple samples, the results of the survey would be recorded (.51, .48, .49, .52…). These would then be put into the form of a histogram (distribution), where the following observations apply:
- the mean of that distribution would be close to .50;
- the distribution would have the shape of a normal distribution;
- the distribution would have a standard deviation equal to
For further discussion of this approach, see accompanying video.
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