File:inf-04-hypothesis-tests-errors.png

Figure file · Hypothesis tests

Left: a two-sided z test of size 0.05. Under H_0 the statistic is \operatorname{N}(0,1), the critical region is the two tails beyond \pm1.960, and an observed z=2.30 has p-value 0.021. Right: under the alternative Z\sim\operatorname{N}(2,1) the same cutoffs split the density into the power, the part beyond them, and the type II error, the part between.

Left: a two-sided z test of size 0.05. Under H_0 the statistic is \operatorname{N}(0,1), the critical region is the two tails beyond \pm1.960, and an observed z=2.30 has p-value 0.021. Right: under the alternative Z\sim\operatorname{N}(2,1) the same cutoffs split the density into the power, the part beyond them, and the type II error, the part between.

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Description. Left: a two-sided z test of size 0.05. Under H_0 the statistic is \operatorname{N}(0,1), the critical region is the two tails beyond \pm1.960, and an observed z=2.30 has p-value 0.021. Right: under the alternative Z\sim\operatorname{N}(2,1) the same cutoffs split the density into the power, the part beyond them, and the type II error, the part between.

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