Question: Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample from a normal distribution with unknown mean. In testing \(H_{0}: \sigma^{2}=\sigma_{0}^{2}\) against \(H_{A}: \sigma^{2}>\sigma_{0}^{2}\), use the critical region defined by \(n S^{2} / \sigma_{0}^{2} \geq c .\) If \(n=13\) and the significance level \(\alpha=.025\), find \(c\).

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