The mean SAT score in mathematics is 482. The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis H0 and the alternative hypothesis H1 that they would use.

In this scenario, the hypothesis test is designed to evaluate whether the graduates of the SAT preparation course have a higher average score in mathematics compared to the national mean of 482. The null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)) would be set up as follows:

- **Null Hypothesis (\(H_0\))**: The mean SAT score of the graduates is equal to the national mean.
  \[
  H_0: \mu = 482
  \]

- **Alternative Hypothesis (\(H_1\))**: The mean SAT score of the graduates is higher than the national mean.
  \[
  H_1: \mu > 482
  \]

This is a one-tailed test because the alternative hypothesis specifies that the mean score is greater than the national mean, rather than simply being different.

Would you like more details or have any questions?

Here are 8 related questions that might interest you:

1. What is the significance level in a hypothesis test, and how is it chosen?
2. How do you calculate the test statistic for a one-sample t-test?
3. What assumptions must be met to conduct a one-sample t-test?
4. What are Type I and Type II errors in hypothesis testing?
5. How do you interpret the p-value in a hypothesis test?
6. What is the power of a hypothesis test, and why is it important?
7. How do sample size and variability affect the outcome of a hypothesis test?
8. Can a one-tailed test be converted into a two-tailed test? If so, how?

**Tip:** Always check if the data meets the assumptions required for the hypothesis test you plan to use, such as normality or homogeneity of variances, to ensure valid results.

Explore hypothesis testing in statistics with a focus on whether graduates of a SAT preparation course score higher on average than the national mean of 482. Understand the setup of null and alternative hypotheses and the significance of one-tailed tests.

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