A study found that 15% of teenagers get the recommended 8 to10 hours of sleep each night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8–10 hours of sleep each school night. Which hypotheses would test if the proportion of students at this high school is different from the proportion in the study?

*H*0:*p* ≠ 0.19, *Ha*:*p* = 0.19

*H*0:*p* ≠ 0.15, *Ha*:*p* = 0.15

*H*0:*p* = 0.19, *Ha*:*p* ≠ 0.19

*H*0:*p* = 0.15, *Ha*:*p* ≠ 0.15

The appropriate hypotheses for testing whether the proportion of students at this high school who get 8–10 hours of sleep each night is different from the proportion found in the study (15%) are as follows:

- The **null hypothesis (H₀)**: The proportion of students at the high school who get 8–10 hours of sleep is the same as the proportion found in the study (15%).
- The **alternative hypothesis (Hₐ)**: The proportion of students at the high school who get 8–10 hours of sleep is different from the proportion found in the study (15%).

So, the correct hypotheses are:

- **H₀:** *p* = 0.15
- **Hₐ:** *p* ≠ 0.15

This corresponds to the last option:

- **H₀:** *p* = 0.15, **Hₐ:** *p* ≠ 0.15

Would you like further details on this? Here are 5 related questions:

1. How do we calculate the test statistic for a hypothesis test about proportions?
2. What significance level is typically used in hypothesis testing?
3. How would you interpret a p-value in this hypothesis test?
4. What is the formula for the standard error in proportion testing?
5. What are Type I and Type II errors in hypothesis testing?

**Tip:** Always ensure you clearly define the population parameter in both your null and alternative hypotheses when conducting hypothesis tests.

A study found that 15% of teenagers get the recommended 8 to 10 hours of sleep each night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8–10 hours of sleep each school night. Which hypotheses would test if the proportion of students at this high school is different from the proportion in the study?

Explore how to test hypotheses regarding the proportion of high school students getting 8 to 10 hours of sleep each night. This statistical problem covers hypothesis testing for proportions using the Z-test. Suitable for students in Grades 10-12.

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