Let's continue to solve all parts of the problem using the given information. We have already established the hypotheses and identified the claim.

Part 1 of 5 (Completed)

• $H_0: \mu \leq 6.9$ (claim)
• $H_1: \mu > 6.9$ (not claim)
• This hypothesis test is a one-tailed test.

Part 2 of 5

(b) Compute the test statistic.

To compute the test statistic for a one-sample t-test, we use the formula: $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$

Where:

• $\bar{x} = 7.4$ (sample mean)
• $\mu_0 = 6.9$ (population mean under null hypothesis)
• $s = 1.2$ (sample standard deviation)
• $n = 13$ (sample size)

Substitute the given values into the formula: $t = \frac{7.4 - 6.9}{1.2 / \sqrt{13}} = \frac{0.5}{1.2 / \sqrt{13}} \approx \frac{0.5}{0.332} \approx 1.506$

So, the test statistic $t \approx 1.506$.

Part 3 of 5

(c) Determine the critical value(s).

Given that the significance level $\alpha = 0.10$ for a one-tailed test and $df = n - 1 = 13 - 1 = 12$, we need to find the critical value from the t-distribution table.

Looking up the t-distribution table for $\alpha = 0.10$ and $df = 12$, the critical value $t_{crit} \approx 1.356$.

Part 4 of 5

(d) Compare the test statistic to the critical value and make a decision to reject or fail to reject the null hypothesis.

• Test statistic $t \approx 1.506$
• Critical value $t_{crit} \approx 1.356$

Since $t > t_{crit}$, we reject the null hypothesis.

Part 5 of 5

(e) State the conclusion in the context of the problem.

Since we reject the null hypothesis, there is enough evidence to support the claim that college students sleep more than 6.9 hours on average on Friday nights to Saturday mornings.

Summary:

• Test statistic: $t \approx 1.506$
• Critical value: $t_{crit} \approx 1.356$
• Decision: Reject the null hypothesis.
• Conclusion: There is enough evidence to say that college students sleep more than 6.9 hours on average.

Would you like details or have any questions? Here are five questions you might find useful:

1. How do you find the critical value for a t-test?
2. What are the assumptions for conducting a one-sample t-test?
3. How does sample size affect the test statistic and critical value?
4. What is the difference between one-tailed and two-tailed tests?
5. How do you interpret the p-value in hypothesis testing?

Tip: When comparing the test statistic to the critical value, ensure you use the correct tail of the distribution based on your hypothesis.