Question

part 4 of 5
(d) when $\alpha = 0.05$ and $n = 25$,
$\chi_{\text{left}}^{2}=13.848$
$\chi_{\text{right}}^{2}=36.415$
try one last time

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 25\), so \(df=25-1 = 24\).

Step2: Find \(\chi_{left}^{2}\)

For a two - tailed test with \(\alpha=0.05\), the area to the left of \(\chi_{left}^{2}\) is \(\frac{\alpha}{2}=0.025\). Using the \(\chi^{2}\) - distribution table or a statistical software, for \(df = 24\), \(\chi_{left}^{2}=\chi_{0.025,24}^{2}=12.401\).

Step3: Find \(\chi_{right}^{2}\)

The area to the right of \(\chi_{right}^{2}\) is \(\frac{\alpha}{2}=0.025\). Using the \(\chi^{2}\) - distribution table or a statistical software, for \(df = 24\), \(\chi_{right}^{2}=\chi_{0.975,24}^{2}=39.364\).

Answer:

\(\chi_{left}^{2}=12.401\), \(\chi_{right}^{2}=39.364\)