# 6.17 t Tests for One Mean: Investigating the Normality Assumption

A discussion of the assumptions of the t test on one mean. (The assumptions are the same as those of the t confidence intervals for one mean.) The assumptions are discussed, and the effect of different violations of the normality assumption is investigated through simulation.

### 2 thoughts on “6.17 t Tests for One Mean: Investigating the Normality Assumption”

1. I’m confused by how the null hypothesis is rejected less often given heavier tails. Don’t heavier tails imply that values are more likely to fall father from the mean and therefore more likely to be outside a z-test confidence interval?

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• I agree that this might be a little surprising at first. But keep in mind that this is a *t* test, and not a z test, and the t statistic uses the sample standard deviation in the formula. When there are heavier tails, we are more likely to get extreme values, and extreme values can really inflate the variance and standard deviation. (For more information about the sampling distribution of the sample variance, see this video of mine: https://www.youtube.com/watch?v=V4Rm4UQHij0) All else being equal, for larger values of s we would need a larger difference between the sample mean and hypothesized mean in order to reject Ho. I believe that’s what’s happening here, but I wholeheartedly agree that this effect is not obvious.

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