1 A random sample of 7 observations of a variable \(X\) are as follows.
$$\begin{array} { l l l l l l l }
8.26 & 7.78 & 7.92 & 8.04 & 8.27 & 7.95 & 8.34
\end{array}$$
The population mean of \(X\) is \(\mu\).
- Test, at the \(10 \%\) significance level, the null hypothesis \(\mu = 8.22\) against the alternative hypothesis \(\mu < 8.22\).
- State an assumption necessary for the test in part (a) to be valid.