Question

(e) when $\alpha = 0.10$ and $n = 14$,
$\chi_{\text{left}}^{2}=\square$
$\chi_{\text{right}}^{2}=\square$

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 14\), then \(df=14 - 1=13\).

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

For a two - tailed test with \(\alpha=0.10\), the area to the left of \(\chi_{left}^{2}\) is \(\frac{\alpha}{2}=0.05\). Using the chi - square distribution table or a statistical software, for \(df = 13\), \(\chi_{left}^{2}=\chi_{1 - 0.05,13}^{2}=\chi_{0.95,13}^{2}=5.892\).

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

The area to the right of \(\chi_{right}^{2}\) is \(\frac{\alpha}{2}=0.05\). Using the chi - square distribution table or a statistical software, for \(df = 13\), \(\chi_{right}^{2}=\chi_{0.05,13}^{2}=22.362\).

Answer:

\(\chi_{left}^{2}=5.892\), \(\chi_{right}^{2}=22.362\)