Test the claim about the population mean, $\mu$, at the given level of significance using the given sample statistics.
Claim: $\mu=30 ; \alpha=0.04 ; \sigma=3.14$. Sample statistics $\bar{x}=28.8, n=57$
Identify the null and alternative hypotheses. Choose the correct answer below.
A. $H_{0}: \mu=30$
B. $\begin{array}{l}H_{0}: \mu> 30 \\ H_{a}: \mu=30\end{array}$
C.
\[
\begin{array}{l}
H_{0}: \mu=30 \\
H_{a}: \mu< 30
\end{array}
\]
D.
\[
\begin{array}{l}
H_{0}: \mu \neq 30 \\
H_{a}: \mu=30
\end{array}
\]
E.
\[
\begin{array}{l}
H_{0}: \mu< 30 \\
H_{a}: \mu=30
\end{array}
\]
\[
\text { F. } \begin{array}{r}
H_{0}: \mu=30 \\
H_{a}: \mu \neq 30
\end{array}
\]
Calculate the standardized test statistic.
The standardized test statistic is
(Round to two decimal places as needed.)

Step 1 ：Identify the null and alternative hypotheses. The null hypothesis is always a statement of no effect or no difference. In this case, the null hypothesis is that the population mean is equal to the claimed value. The alternative hypothesis is the opposite of the null hypothesis. Since the sample mean is less than the claimed value, we are testing whether the population mean is less than the claimed value. Therefore, the null and alternative hypotheses are as follows: \[H_{0}: \mu=30\] \[H_{a}: \mu<30\]

Step 2 ：Calculate the standardized test statistic using the formula: \[Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\] where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and \(n\) is the sample size. Substituting the given values, we get \[Z = \frac{28.8 - 30}{3.14 / \sqrt{57}}\]

Step 3 ：The calculated value of the standardized test statistic is approximately -2.89.

Step 4 ：Final Answer: The null and alternative hypotheses are: \[H_{0}: \mu=30\] \[H_{a}: \mu<30\] The standardized test statistic is \(\boxed{-2.89}\).