To analyze this hypothesis testing question:

Problem Breakdown:

The claim is that the new sedan, the Libra, will average better than 32 miles per gallon.

• This means the alternative hypothesis ($H_1$) would test whether the mean mileage, $\mu$, is greater than 32.
• The null hypothesis ($H_0$) is the opposite of this claim, stating that $\mu$ is less than or equal to 32.

Correct Answer:

The hypotheses are:

• $H_0: \mu \leq 32$ (the car does not average better than 32 mpg)
• $H_1: \mu > 32$ (the car averages better than 32 mpg)

Thus, the correct choice is C:

• $H_0: \mu \leq 32$
• $H_1: \mu > 32$

Do you need additional details or help with hypothesis testing steps?
Here are 5 related questions you might explore:

1. How do you determine the rejection region for a one-tailed test like this?
2. What is the role of the significance level ($\alpha$) in hypothesis testing?
3. What test statistic would you use for this scenario?
4. How does sample size affect the validity of hypothesis testing?
5. When should you use a one-tailed test versus a two-tailed test?

Tip: Always align the alternative hypothesis with the claim being tested to ensure clarity.