Wiki Page, Math 13 - Perez Sandbox : Module 24 - Hypothesis Test for a Population Mean Practice Solutions (4a of 5)

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2026-01-17T21:15:42-08:00

Here is the hypothesis test covered in the previous quiz. If you did not score a 100%, review these answers as another worked example.

Scenario: Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.

Checking conditions: First we consider whether this a random sample from the population of interest. Since we are told that this is a random sample of students at LMC, we conclude that we have a random sample from the population of interest (all students at LMC). Next we consider whether the conditions for the use of a t-model are met. The sample size is 43. This is large enough to proceed with the t-test regardless of the shape of the distribution of sleep hours in the LMC student population.

Test statistic:

So the test statistic is .

P-value: Set the degrees of freedom to 43 − 1 = 42. Since the alternative hypothesis is , this is a two-tailed test. Double the area in the right tail: 2(0.1615) = 0.323. This is the P-value. Here is a picture of the applet showing these results.

Conclusion: Since the P-value of about 0.323 is larger than the significance level of 0.05, we fail to reject .
Conclusion in context: The data from this study does not suggest that the amount of sleep for LMC students differs from the national average of 6.9 hours (P-value is about 0.323). This sample of LMC students sleep on average 7.12 hours, but the difference is not statistically significant and could be explained by predictable variation that occurs in random sampling.

General comment: Recall that we can never support . We either reject and accept , or we fail to reject .

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