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st: guessing mean of bounded variable with 1:30 sampling ratio
I have a population of N=12000. I want to know the mean (and possibly the standard deviation) of a variable x, bounded between 1 and 7. I took a (let's suppose random) sample of n=400 and estimated mean = 3.14 (standard error = .15) and standard deviation = 2.28. The sample strongly departs from normality. Can I trust such estimates? How much? Can I attach a p-value to them? I need to state formally that, despite a ridicolous response rate, my research is not that bad.
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