https://file.aiquickdraw.com/mathbot/file/1721680298326wp2cg08n.png

Let's solve part (a) and continue from there.

### Part 1 of 5

(a) State the hypotheses and identify the claim.

Given the problem, we need to state the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).

- **Null Hypothesis (\( H_0 \))**: The average number of hours slept by college students is not more than 6.9 hours.
  \[
  H_0: \mu \leq 6.9
  \]

- **Alternative Hypothesis (\( H_1 \))**: The average number of hours slept by college students is more than 6.9 hours.
  \[
  H_1: \mu > 6.9
  \]

- **Type of Test**: This is a right-tailed test because the alternative hypothesis is testing if the mean is greater than a specific value.

### Explanation for Hypotheses

The claim is that college students sleep more than 6.9 hours on average. Therefore, the null hypothesis states the opposite to test against the claim.

#### Summary for Part (a):

- \( H_0: \mu \leq 6.9 \)
- \( H_1: \mu > 6.9 \)
- This hypothesis test is a right-tailed test.

Would you like details or have any questions? Here are the next steps we can work on:

1. Calculate the test statistic.
2. Determine the critical value(s).
3. Compare the test statistic to the critical value(s).
4. Make a decision to reject or fail to reject the null hypothesis.
5. State the conclusion in the context of the problem.

**Tip**: Remember that for hypothesis testing, the null hypothesis is assumed true until evidence suggests otherwise.

Explore hypothesis testing with a focus on college students' average sleep hours. Learn about null and alternative hypotheses, right-tailed tests, and the process of statistical hypothesis testing.

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