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.