To test $\mathrm{H}_{0}: \sigma=2.3$ versus $\mathrm{H}_{1}: \sigma>2.3$, a random sample of size $n=16$ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d). (a) If the sample standard deviation is determined to be $s=2.1$, compute the test statistic. $\chi_{0}^{2}=$ (Round to three de gima places as needed.)

Step 1 ：Given that the sample size \(n = 16\), the sample standard deviation \(s = 2.1\), and the standard deviation under the null hypothesis \(\sigma = 2.3\).

Step 2 ：The test statistic for a hypothesis test about a population standard deviation or variance is a Chi-Square statistic, which is calculated using the formula: \[\chi_{0}^{2} = \frac{(n - 1)s^{2}}{\sigma^{2}}\]

Step 3 ：Substitute the given values into the formula: \[\chi_{0}^{2} = \frac{(16 - 1)2.1^{2}}{2.3^{2}}\]

Step 4 ：Calculate the test statistic to get \(\chi_{0}^{2} = 12.504725897920608\)

Step 5 ：Round the test statistic to three decimal places to get \(\chi_{0}^{2} = 12.505\)

Step 6 ：So, the test statistic is \(\boxed{12.505}\)