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Math — Hypothesis Testing

z- and t-statistics, decision rule and a confidence interval.

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z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}

t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}

\text{reject } H_0 \text{ if } p < \alpha

\bar{x} \pm z^*\frac{\sigma}{\sqrt{n}}