One-sample \(t\) Procedures.
Parameter: \(\mu\) = the population mean
To test \(H_0: \mu = \mu_0\)
Standardized (test) statistic:
\begin{equation*}
t_0 = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}
\end{equation*}
Degrees of freedom = \(n - 1\)
\begin{equation*}
\bar{x} \pm t_{n-1}^* \frac{s}{\sqrt{n}}
\end{equation*}
Technical conditions: These procedures are considered valid if the sample distribution is reasonably symmetric or the sample size is at least 30; and the data are independent and identical observations from a random process or are from a large population (\(N \gt 20 n\)).
