Test the claim about the population mean, $\mu$, at the given level of significance using the given sample statistics. Claim: $\mu \neq 7000 ; \alpha=0.02 ; \sigma=369$. Sample statistics: $\bar{x}=6600, n=44$ A. $\mathrm{H}_{0}: \mu \neq 7000$ $H_{a}: \mu \geq 7000$ C. $\mathrm{H}_{0}: \mu \leq 7000$ $\mathrm{H}_{\mathrm{a}}: \mu \neq 7000$ E. $H_{0}: \mu \geq 7000$ $\mathrm{H}_{\mathrm{a}}: \mu \neq 7000$ B. $H_{0} \cdot \mu \neq 7000$ $H_{a}: \mu \leq 7000$ D. \[ \begin{array}{l} H_{0}: \mu=7000 \\ H_{a}: \mu \neq 7000 \end{array} \] 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 (Round to two decimal places as needed.)

Step 1 ：The claim is that the population mean, \(\mu\), is not equal to 7000. The level of significance is \(\alpha = 0.02\). The sample statistics are: sample mean \(\bar{x} = 6600\), sample size \(n = 44\), and standard deviation \(\sigma = 369\).

Step 2 ：The null hypothesis, \(H_0\), is the statement that the parameter takes the value specified in the claim. The alternative hypothesis, \(H_a\), is the statement that the parameter takes a value that contradicts the claim.

Step 3 ：In this case, the null hypothesis is \(H_0: \mu = 7000\) and the alternative hypothesis is \(H_a: \mu \neq 7000\).

Step 4 ：The standardized test statistic for a hypothesis test of a population mean is a z-score (z). The z-score is calculated by subtracting the population mean from the sample mean, and then dividing by the standard deviation divided by the square root of the sample size.

Step 5 ：Using the given values, the z-score is calculated as follows: \(z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\). Substituting the given values, we get \(z = \frac{6600 - 7000}{369 / \sqrt{44}}\).

Step 6 ：The calculated z-score is -7.19. This value is the standardized test statistic. It represents how many standard deviations the sample mean is away from the population mean under the null hypothesis.

Step 7 ：Final Answer: The standardized test statistic is \(\boxed{-7.19}\).