The national average SAT score is roughly 1500 . We would like to see if the high school seniors who apply to Duke have higher than average SAT scores. We randomly sample 100 applicants' files and record their SAT scores. Which of the following is the correct set of hypotheses for this research question? Hint: think about how many samples we have data from. OH \( H_{0}: x=1500 ; H_{A}: x>1500 \) H \( H_{0}: P=1500 ; H_{A}: P>1500 \) \( H_{0}: \mu_{\text {Duke }}=\mu=1500 ; H_{A}: \mu>1500 \) \( H_{0}: \mu=1500 ; H_{A}: \mu \neq 1500 \)

To test whether the high school seniors applying to Duke have higher than average SAT scores, we need to focus on the population mean SAT score of these specific applicants. Therefore, the correct set of hypotheses is: \( H_{0}: \mu_{\text {Duke }}=1500 \); \( H_{A}: \mu_{\text {Duke }}>1500 \) This means we are stating that the average SAT score of Duke applicants is equal to the national average, while the alternative hypothesis suggests it is greater than that average. Now, when conducting hypothesis tests, a common mistake is confusing the population parameters with sample statistics. Remember, the null hypothesis always refers to the population parameter (like \(\mu\) for mean), rather than using sample data averages. Be sure to clearly differentiate between the sample mean and the population mean in your analysis!