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Confidence intervals and hypothesis tests are tightly related, as the former can be inverted to yield the latter and vice versa. Given a fixed type 1 error equal to C (usually 5%), if a hypothesis test rejects the null hypothesis (that a statistic is equal to zero), then the 1-C (95%) confidence intervals won't include the zero. Notice that the pooled standard deviation estimate is obtained by pooling the variability for the two samples. In the next recipe, we will discuss what happens when this assumption is violated.