Well, the fact that the population distribution is skewed to the left should violate the assumption of normality, so I wouldn't use a Normal to calculate margin of error.

Normally, we use the t-distribution because it's got heavier tails, so it's more appropriate when we're less certain about the distribution (this is usually when we have a small sample size, which you do here). But it doesn't address the skew.

Personally, if I were tackling this problem I would transform the data by raising it to a power, to counteract the skew and make it more normally / symmetrically distributed. This would come under the category of "Advanced Statistical Techniques" here I should expect.

Mar 5th, 2015

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