The image you uploaded seems to be a question related to hypothesis testing for SAT scores in mathematics. You are asked to state the null hypothesis $H_0$ and the alternative hypothesis $H_1$.

Based on the information provided:

• The mean SAT score in mathematics is 529.
• The founders of a nationwide SAT preparation course claim that their students score higher than the national mean.

In hypothesis testing, the null hypothesis $H_0$ represents the statement of no effect or no difference, while the alternative hypothesis $H_1$ reflects the claim or assertion that is being tested.

Null Hypothesis ($H_0$):

The null hypothesis would state that the SAT scores of students in the course are equal to the national mean (529).

So, the null hypothesis is: $H_0: \mu = 529$

Alternative Hypothesis ($H_1$):

The alternative hypothesis would reflect the claim that students in the course score higher than the national mean. Therefore, the alternative hypothesis is: $H_1: \mu > 529$

Do you need further details or clarification on hypothesis testing? Let me know if you have any questions.

Here are some related questions to help you expand on this topic:

1. What is the role of the p-value in hypothesis testing?
2. How do you decide whether to reject or fail to reject the null hypothesis?
3. What is the significance level (alpha) in hypothesis testing, and how is it determined?
4. Can the null hypothesis ever be "proven"? Why or why not?
5. What is a Type I error in hypothesis testing?

Tip: Always remember that the null hypothesis assumes no effect, while the alternative hypothesis tests for an effect or difference based on the research question.