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The distributions we'll use for hypothesis testing are the same ones we used for confidence intervals:
\begin{itemize}
\item To test a claim about means when the population standard deviation is known, use the normal distribution with a mean of $\mu$ and a standard deviation of $\sigma/\sqrt{n}$.
We'll have a z test statistic. Remember, to find a z score, subtract the mean and divide by the standard deviation:
\[z = \dfrac{\overline{x}-\mu}{\sigma/\sqrt{n}}\]
\item To test a claim about means when the population standard deviation is unknown, use the t distribution with a mean of $\mu$ and a standard deviation of $s/\sqrt{n}$.
We'll have a t test statistic.
\[t = \dfrac{\overline{x}-\mu}{s/\sqrt{n}}\]
\item To test a claim about proportions, use the normal distribution with a mean of $p$ and a standard deviation of $\sqrt{\dfrac{p(1-p)}{n}}$.
We'll have a z test statistic. Remember, to find a z score, subtract the mean and divide by the standard deviation:
\[z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\]
\end{itemize}
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