You are running for office and your pollster polled hundred people. 56 of them claimed they will vote for you. Can you relax?

You are running for office and your pollster polled hundred people. 56 of them claimed they will vote for you. Can you relax?



Quick:
- Intervals take the form p±z×1n×p×(1−p)−−−−−−−−−−−−−√p±z×1n×p×(1−p)
- We know that p(1−p)p(1−p) is maximized at 1212 and z=1.96z=1.96 is the relevant quantile for a 95% confidence interval
- So: p±1n√p±1n is a quick estimate for pp
- Here: 1100√=0.11100=0.1 so 95% of the intervals would be [46,66][46,66]
- It's not enough!

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