A random sample of $n = 6$ observations from a normal population produced the following measurements: $\begin{array}{llllll} 7& 9& 5& 2& 7& 4 \cr \end{array}$
Do the data provide sufficient evidence to indicate that $\sigma^2 < 2$? Use $\alpha = 0.05$, and compute the following:
(a) $\ $ sample standard deviation $s =$
(b) $\ $ test statistic $\chi^2 =$
(c) $\ $ critical $\chi^2_{\alpha} =$

The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that $\sigma^2 \geq 2$.
B. We can reject the null hypothesis that $\sigma^2 = 2$ in favor of the alternative $\sigma^2 < 2$.