Problem
Español A car leasing firm's records indicate that the mean number of miles driven annually in its cars has been about 14,750 miles. The firm suspects that this number has decreased this past year. Suppose that the firm wishes to choose a small sample of driving distances from the past year and carry out a hypothesis test for its suspicion. State the null hypothesis $\mathrm{H}_{0}$ and the alternative hypothesis $H_{1}$ that it would use for this test. \[ \begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array} \] \begin{tabular}{ccc} \hline$\mu$ & $\bar{x}$ & $p$ \\ $\hat{p}$ & $\sigma$ & $s$ \\ $\square \square$ & & $\square<\square$ \\ $\square \leq \square$ & $\square>\square$ & $\square \geq \square$ \\ $\square=\square$ & $\square \neq \square$ & \end{tabular}
Solution
Step 1 ：The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance. In this case, the null hypothesis would be that the mean number of miles driven annually in the firm's cars is still about 14,750 miles.
Step 2 ：The alternative hypothesis, denoted by H1, is the hypothesis that sample observations are influenced by some non-random cause (for example, our cars are being driven less). In this case, the alternative hypothesis would be that the mean number of miles driven annually in the firm's cars has decreased from 14,750 miles.
Step 3 ：Final Answer: \n\[\begin{array}{l}H_{0}: \mu = 14750 \H_{1}: \mu < 14750\end{array}\]
