A car leasing firm's records indicate that the mean number of miles driven annually in its cars has been about 17,750 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 H0 and the alternative hypothesis H1 that it would use for this test.

In this scenario, the car leasing firm wants to test whether the mean number of miles driven annually in its cars has decreased from the previous mean of 17,750 miles. The hypotheses for this test can be set up as follows:

- The **null hypothesis (\(H_0\))** is a statement of no change or no effect. In this case, it asserts that the mean number of miles driven annually has not decreased.

- The **alternative hypothesis (\(H_1\))** reflects the firm's suspicion that the mean number of miles driven annually has decreased.

Therefore, the hypotheses can be stated as:

- **\(H_0\):** \(\mu \geq 17{,}750\)

- **\(H_1\):** \(\mu < 17{,}750\)

Where \(\mu\) represents the mean number of miles driven annually in the firm's cars this past year.

**Do you want more details or have any questions?**

Here are 8 related questions:

1. What statistical test is appropriate for comparing the mean of a sample to a known value?
2. How does the choice of significance level (\(\alpha\)) affect the outcome of a hypothesis test?
3. How is the standard deviation used in hypothesis testing for means?
4. What is the p-value, and how is it interpreted in the context of hypothesis testing?
5. What are the steps involved in conducting a hypothesis test?
6. How can we ensure the sample chosen is representative of the population?
7. What could be the reasons for a decrease in the mean number of miles driven annually?
8. How might the leasing firm use the results of this hypothesis test to inform business decisions?

**Tip:** Clearly defining your hypotheses and choosing the right test is crucial for obtaining meaningful results in hypothesis testing.

Explore hypothesis testing to determine if the mean number of miles driven annually has decreased from 17,750 miles. Understand null and alternative hypotheses, statistical significance, and interpreting results. Suitable for college-level statistics and business analysis.

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