K
Test the claim about the population mean, $\mu$, at the given level or sigrl
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. $H_{0}: \mu> 30$
$\mathrm{H}_{\mathrm{a}}: \mu> 30$
$\mathrm{H}_{\mathrm{a}} \cdot \mu=30$
C. $\mathrm{H}_{0} \cdot \mu=30$
D. $\mathrm{H}_{0}: \mu \neq 30$
$H_{a}: \mu< 30$
$H_{a}: \mu=30$
E. $\mathrm{H}_{0}: \mu< 30$
F. $H_{0}, \mu=30$
$H_{a} \mu=30$
$H_{a}: \mu \neq 30$

Step 1 ：Identify the null and alternative hypotheses.

Step 2 ：The null hypothesis is always a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove. In this case, the null hypothesis is that the population mean is equal to the claimed value, which is 30. So, the null hypothesis is \(H_{0}: \mu=30\).

Step 3 ：The alternative hypothesis is what you might believe if the null hypothesis is concluded to be untrue. The claim is that the population mean is 30, and the sample mean is less than 30. So, we are testing if the population mean is less than 30. Therefore, the alternative hypothesis is \(H_{a}: \mu<30\).

Step 4 ：So, the correct answer is \(H_{0}: \mu=30\) and \(H_{a}: \mu<30\).

Step 5 ：Final Answer: \(\boxed{D. H_{0}: \mu=30, H_{a}: \mu<30}\)