Problem
Part 1 of 4 Points: 0 of Test the claim about the population mean $\mu$ at the level of significance $\alpha$. Assume the population is normally distributed. Claim: $\mu \geq 1473 ; \alpha=0.02 ; \sigma=28$. Sample statistics: $\bar{x}=1466, n=25$ Identify the null and alternative hypotheses. Choose the correct answer. A. \[ \begin{array}{l} H_{0}: \mu \geq 1473 \\ H_{a}: \mu<1473 \end{array} \] C. \[ \begin{array}{l} H_{0}: \mu>1466 \\ H_{a}: \mu \leq 1466 \end{array} \] E. \[ \begin{array}{l} H_{0}: \mu>1473 \\ H_{a}: \mu \leq 1473 \end{array} \] B. \[ \begin{array}{l} H_{0}: \mu<1466 \\ H_{a}: \mu \geq 1466 \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu \geq 1466 \\ H_{a}: \mu<1466 \end{array} \] F. \[ \begin{array}{l} H_{0}: \mu<1473 \\ H_{\mathrm{a}}: \mu \geq 1473 \end{array} \]
Solution
Step 1 ：Identify the null and alternative hypotheses. The null hypothesis (H0) is a statement of no effect or no difference and is assumed to be true until we have enough evidence to reject it. The alternative hypothesis (Ha) is a statement of an effect or difference and we are trying to find evidence to support this.
Step 2 ：In this case, the claim is that the population mean is greater than or equal to 1473. This is our null hypothesis. The alternative hypothesis is the opposite of the null hypothesis. So, the alternative hypothesis is that the population mean is less than 1473.
Step 3 ：Final Answer: \(\boxed{H_{0}: \mu \geq 1473, H_{a}: \mu<1473}\)
