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What is the sample size if in theory 19 out of 20 cases the results from a poll should differ by no more than 1 percent in either direction from what would have been obtained by polling all Americans?
Vputhusseril
Your confidence level is 19/20=95%
1% is your margin of error
'either direction' means it's two-sided
Sample size, n, should be larger than (zalpha/2)2p(1-p)/m2
where
zalpha/2 is the upper critical value of the normal distribution. For your level of confidnce (95%) alpha=0.05. So alpha/2=0.025, making z=1.96
p is your 'best guess' about the true value of the proportion. You can estimate with a pilot study, or set to 50% which will maximise the sample size possibly much larger than required.
m is your margin of error (1%)
So choose a sample size of n>=(1.96)2*(0.5)2/0.012=9604
However, this will result in a test with only 50% power (i.e. probability of not getting a false negative is 50%). Typically power is set to around 80%. To increase power the sample size would have to be even larger.
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