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 $\mu$.\\
(a) Test, at the $10 \%$ significance level, the null hypothesis $\mu = 8.22$ against the alternative hypothesis $\mu < 8.22$.\\

(b) State an assumption necessary for the test in part (a) to be valid.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2021 Q1}}