Test the claim about the population mean, $\boldsymbol{\mu}$, at the given level of significance using the given sample statistics. Claim: $\mu \neq 7000 ; \alpha=0.02 ; \sigma=369$. Sample statistics: $\bar{x}=6600, n=44$ E. \[ \begin{array}{l} H_{0}: \mu \geq 7000 \\ H_{a}: \mu \neq 7000 \end{array} \] F. \[ \begin{array}{l} H_{0}: \mu \neq 7000 \\ H_{a}: \mu=7000 \end{array} \] Calculate the standardized test statistic. The standardized test statistic is -7.19 (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. The critical value is B. The critical values are \pm

Step 1 ：State the null and alternative hypotheses. The null hypothesis is that the population mean is equal to 7000, and the alternative hypothesis is that the population mean is not equal to 7000.

Step 2 ：Calculate the standardized test statistic using the formula \(Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\). In this case, \(\bar{x} = 6600\), \(\mu = 7000\), \(\sigma = 369\), and \(n = 44\). The calculated standardized test statistic is -7.19.

Step 3 ：Determine the critical value(s). The critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. The critical value depends on the level of significance, which is given as \(\alpha = 0.02\). Since the claim is that \(\mu \neq 7000\), this is a two-tailed test, so we need to find the critical values that cut off the upper and lower 0.01 (0.02/2) of the distribution. The critical values are -2.33 and 2.33.

Step 4 ：Compare the test statistic to the critical value. The standardized test statistic is -7.19, which is less than the critical value of -2.33. This means that the test statistic falls in the rejection region, so we reject the null hypothesis.

Step 5 ：Final Answer: The standardized test statistic is \(\boxed{-7.19}\) and the critical values are \(\boxed{-2.33}\) and \(\boxed{2.33}\).