Problem
A used car dealer says that the mean price of a three-year-old sports utility vehicle is $\$ 21,000$. You suspect this claim is incorroct and find that a randorn sample of 23 simlar vehicles has a mean price of $\$ 21,628$ and a standard deviation of $\$ 1940$. Is there enough evidence to rejoct the claim at $\alpha=0.10$ ? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim muthernatically and identify $\mathrm{H}_{0}$ and $\mathrm{H}_{2}$. Which of the following correctly states $\mathrm{H}_{0}$ and $\mathrm{H}_{2}$ ? A. \[ \begin{array}{l} \mathbf{H}_{0}: \mu=\$ 21,000 \\ H_{\mathbf{d}}: \mu \neq \$ 21,000 \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu 2 \$ 21,000 \\ H_{0}: \mu<\$ 21,000 \end{array} \] B. \[ \begin{array}{l} H_{0}-\mu=\$ 21,000 \\ H_{a} \mu>\$ 21,000 \end{array} \] E. \[ \begin{array}{l} H_{0}: \mu=\$ 21,000 \\ H_{\mu}: \mu<\$ 21,000 \end{array} \] c. \[ \begin{array}{l} H_{0}: \mu \neq \$ 21,000 \\ H_{a}: \mu=\$ 21,000 \end{array} \] F. \[ \begin{array}{l} H_{0}: \mu>\$ 21,000 \\ H_{0}: \mu \leq \$ 21,000 \end{array} \]
Solution
Step 1 ：The null hypothesis (H0) is usually 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 mean price of a three-year-old sports utility vehicle is $21,000.
Step 2 ：The alternative hypothesis (Ha) is the statement that the researcher wants to prove. It is the opposite of the null hypothesis. In this case, the alternative hypothesis is that the mean price of a three-year-old sports utility vehicle is not $21,000.
Step 3 ：So, the correct answer should be option A.
Step 4 ：Final Answer: \(\boxed{A}\)
