To test $H_{0}: \sigma=2.2$ versus $H_{1}: \sigma<2.2$, a random sample of size $n=19$ is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be $s=2.2$, compute the test statistic. $\chi_{0}^{2}=\square$ (Round to three decinnal places as needed.)

Step 1 ：We are given a hypothesis test $H_{0}: \sigma=2.2$ versus $H_{1}: \sigma<2.2$. A random sample of size $n=19$ is obtained from a population that is known to be normally distributed.

Step 2 ：The sample standard deviation is determined to be $s=2.2$.

Step 3 ：The test statistic for a hypothesis test about a population standard deviation or variance is a chi-square statistic. The formula for the test statistic when testing a claim about a population standard deviation or variance is: \[\chi_{0}^{2} = \frac{(n-1)s^{2}}{\sigma^{2}}\] where: \[\chi_{0}^{2}\] is the test statistic, $n$ is the sample size, $s$ is the sample standard deviation, and $\sigma$ is the population standard deviation.

Step 4 ：Substituting the given values into the formula, we get: \[\chi_{0}^{2} = \frac{(19-1)2.2^{2}}{2.2^{2}}\]

Step 5 ：Solving the above expression, we find that the test statistic is \(\boxed{18.000}\).