Test the claim about the population mean, $\mu$, at the given level of significance using the given sample statistics. Claim: $\mu=30 ; \alpha=0.08 ; \sigma=3.06$. Sample statistics: $\bar{x}=29.8, n=75$ C. \[ \begin{array}{l} H_{0}: \mu=30 \\ H_{a}: \mu<30 \end{array} \] E. \[ \begin{array}{l} H_{0}: \mu \neq 30 \\ H_{a}: \mu=30 \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu<30 \\ H_{a}: \mu=30 \end{array} \] F. \[ \begin{array}{l} H_{0}: \mu=30 \\ H_{a}: \mu \neq 30 \end{array} \] Calculate the standardized test statistic. The standardized test statistic is -0.57 . (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 hypotheses. The first step is to state the null hypothesis and the alternative hypothesis.

Step 2 ：\[H_{0}: \mu=30\]

Step 3 ：\[H_{a}: \mu \neq 30\]

Step 4 ：Calculate the standardized test statistic. The formula for the standardized test statistic in a z-test is \(Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\).

Step 5 ：\[Z = \frac{29.8 - 30}{3.06 / \sqrt{75}} = -0.57\]

Step 6 ：Determine the critical value(s). The critical value is the value that the test statistic must exceed in order for the null hypothesis to be rejected. Since we are considering a two-tailed test, there will be two critical values, one positive and one negative. The critical values can be found using the z-table for the given level of significance, \(\alpha=0.08\).

Step 7 ：The critical values are approximately \(\pm 1.75\)

Step 8 ：Since the standardized test statistic is less than the positive critical value and greater than the negative critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that the population mean is not 30.

Step 9 ：\[\boxed{\text{Final Answer: The correct hypotheses are } H_{0}: \mu=30 \text{ and } H_{a}: \mu \neq 30. \text{ The standardized test statistic is } -0.57. \text{ The critical values are approximately } \pm 1.75. \text{ Since the standardized test statistic is within the range of the critical values, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that the population mean is not 30.}}\]