+ \subsection*{Distribution of sample mean}
+
+ If \(X \sim \operatorname{N}(\mu, \sigma)\), then distribution of sample mean \(\overline{X}\) is also normal with \(\overline{X} \sim \operatorname{N}(\mu, \frac{\sigma}{\sqrt{n}}\).
+
+ \subsection*{Statistical significance}
+
+ Significance level is denoted by \(\alpha\).
+
+ If \(p<\alpha\), null hypothesis is \textbf{rejected} \\
+ If \(p>\alpha\), null hypothesis is \textbf{accepted}
+
+ \subsection*{\(z\)-test}
+
+ Hypothesis test for a mean of a sample drawn from a normally distributed population with a known standard deviation.
+
+ \subsubsection*{\colorbox{cas}{\textbf{On CAS:}}}
+
+ Menu \(\rightarrow\) Statistics \(\rightarrow\) Calc \(\rightarrow\) Test. \\
+ Select \textit{One-Sample Z-Test} and \textit{Variable}, then input:
+ \begin{itemize}
+ \item \(\mu\) condition - same operator as \(H_1\)
+ \item \(\mu_0\) - expected sample mean (null hypothesis)
+ \item \(\sigma\) - standard deviation (null hypothesis)
+ \item \(\overline{x}\) - sample mean
+ \item \(n\) - sample size
+ \end{itemize}