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. $\chi_{0}^{2}=12.505$ (Round to hede decimal places as needed.) (b) If the researcher decides to test this hypothesis at the $\alpha=0.05$ level of significance, determine the critical value. $\chi_{0.05}^{2}=\square($ Round to three decimal places as needed.)

Step 1 ：Given that the sample size (n) is 16, the sample standard deviation (s) is 2.1, and the hypothesized population standard deviation (σ) is 2.3.

Step 2 ：We can calculate the test statistic using the formula \(\chi^{2} = \frac{(n - 1)s^{2}}{\sigma^{2}}\). Substituting the given values, we get \(\chi^{2} = \frac{(16 - 1)2.1^{2}}{2.3^{2}} = 12.505\).

Step 3 ：The test statistic is \(\boxed{12.505}\).

Step 4 ：To find the critical value, we look at the chi-square distribution table with n - 1 degrees of freedom at the 0.05 level of significance. In this case, the degrees of freedom (df) is 15 and the significance level (α) is 0.05.

Step 5 ：From the chi-square distribution table, we find that the critical value is 24.996.

Step 6 ：The critical value is \(\boxed{24.996}\).