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# 30 - Two-sample problems 1 The goal of inference is to...

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Two-sample problems: 1. The goal of inference is to compare the responses to two treatments or to compare the characteristics of two populations. 2. We have a separate sample from each treatment or each population. Conditions for inference comparing two means: 1. We have two SRSs, from two distinct populations. The samples are independent. That is, one sample has no influence on the other. Matching violates independence, for example. We measure the same response variable for both samples. 2. Both populations are Normally distributed. The means and standard deviations of the populations are unknown. In practice, it is enough that the distributions have similar shapes and that the data have no strong outliers. The two-sample t statistic has approximately a t distribution. It does not have exactly a t distribution even if the populations are both exactly Normal. In practice, however, the approximation is very accurate.

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