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August 22nd, 2016, 05:11 PM   #1
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Would People Know If Results Are Within A 95% Confidence Interval 95% Of The Time?

I was reading about political polling and margin of error. I'm not saying statisticians are wrong about margin of error, but what if hypothetically polls in general are within the 95% confidence interval only 75% of the time? Without asking the entire population, how would people know if the actual margin of error required for a 95% confidential interval was significantly more or less than what people think?
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August 23rd, 2016, 07:15 AM   #2
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For proportions, we can assume that the underlying distribution is binomial, which is approximately normal if the sample size is large. That's why we can approximate the distribution of the sample proportion using the normal distribution, transform it into a Z-statistic and compute the confidence interval.

BTW, the more precise interpretation of the meaning of a 95% confidence interval is that in the long run, 95% of the identically-conducted studies will yield a confidence interval that contains the desired parameter.
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