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.