Question

(b) when $\alpha = 0.05$ and $n = 13$,
$\chi_{left}^{2} =$
$\chi_{right}^{2} =$

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 13\), then \(df=13-1 = 12\).

Step2: Find the left - tailed \(\chi^{2}\) value

For a two - tailed test with \(\alpha=0.05\), the area in the left tail is \(\frac{\alpha}{2}=0.025\). Looking up in the \(\chi^{2}\) distribution table with \(df = 12\), \(\chi_{left}^{2}=\chi_{0.025,12}^{2}=4.404\).

Step3: Find the right - tailed \(\chi^{2}\) value

The area in the right tail is \(\frac{\alpha}{2}=0.025\). Looking up in the \(\chi^{2}\) distribution table with \(df = 12\), \(\chi_{right}^{2}=\chi_{0.975,12}^{2}=23.337\).

Answer:

\(\chi_{left}^{2}=4.404\), \(\chi_{right}^{2}=23.337\)