Question

to determine if there is a relationship between grade performance and extracurricular participation, north carolina state conducted a study of 112 students, recording the number of students in each of three extracurricular categories and each of two grade categories. here are the results: table with data: low extra - curricular participation: good grades 11, poor grades 2; moderate extra - curricular participation: good grades 68, poor grades 23; high extra - curricular participation: good grades 3, poor grades 5 source: felder, et al., \a study of student performance in an introductory chemical engineering course,\ 1992 asee annual conference proceedings, pp. 1516 - 1519. the expected count of students with high extracurricular participation and good grades is the number of students that you would expect to see assuming that which of the following is correct? check all that apply. a. the conditions that allow us to safely use the chi - squared procedure are met. b. extracurricular participation and grade performance are related. c. extracurricular participation and grade performance are independent. d. the null hypothesis of the chi - squared test for independence in this case is true.

Explanation:

The expected counts in a chi - squared test for independence are calculated assuming the null hypothesis is true, which states that the two categorical variables (extracurricular participation and grade performance) are independent. The conditions for using the chi - squared procedure are not related to what the expected counts assume. If we assume the variables are related, we cannot calculate expected counts in the standard way for the independence test.

Answer:

C. Extracurricular participation and grade performance are independent.
D. The null hypothesis of the chi - squared test for independence in this case is true.