Final answer:
The expected count of students with high extracurricular participation and good grades can be determined using a chi-squared test for independence, which checks if there is a relationship between extracurricular participation and grade performance.
Step-by-step explanation:
The expected count of students with high extracurricular participation and good grades can be determined by performing a chi-squared test for independence. In this case, the null hypothesis of the test would be that extracurricular participation and grade performance are independent. If the test results in a significant p-value, we would reject the null hypothesis and conclude that there is a relationship between extracurricular participation and grade performance. Therefore, the correct statement is: Extracurricular participation and grade performance are related.
However, it's important to note that the chi-squared test can only determine if there is a relationship between the two variables, but it cannot establish causation. So even if we find a relationship, we cannot say that extracurricular participation directly causes better grades.