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September 28th, 2012, 12:37 PM   #1
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How would you figure out the confidence interval given...

Lets say you want to test an email version for a marketing campaign, assuming a 5% click through ratio with 20,000 email addresses sample size.
What would be the lower and upper bounds at 90% confidence interval if you were only willing to accept
What would be the lower and upper bounds @ 90% confidence interval you would accept as “equal to the baseline” response rate? What about at 95%?

Please explain how you would do something like this?
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September 28th, 2012, 07:09 PM   #2
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Re: How would you figure out the confidence interval given..

Hey fstep.

If you are testing a proportion (i.e. estimating this from some data), then if you have a huge sample size: your distribution would correspond to an asymptotic distribution where [p - p_hat]/SE(p_hat) ~ N(0,1) where p_hat = X/n and SE(p_hat) = SQRT(p_hat*(1 - p_hat)/n) where n is the sample size and X is the number of successes.

Since this is a normal distribution, you need to use a computer to find a value where P(-a < Z < a) = 0.9 for some a. For a 95% interval, the a is roughly 1.96 so it means for a 90% interval it will be slightly lower (but not a great deal).

Now if you figure out this a (search for a Normal probability calculator on google) then your interval will be [p_hat - a*SE(p_hat), p_hat + a*SE(p_hat)] for some given a where this a corresponds to P(-a < Z < a) = 0.9 where a > 0 [It has to be].
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