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August 22nd, 2016, 05:11 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 637 Thanks: 85  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?

August 23rd, 2016, 07:15 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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 Zstatistic 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 identicallyconducted studies will yield a confidence interval that contains the desired parameter. 

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