Question

question 4
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:

	good grades	poor grades
moderate extra - curricular participation	68	20
high extra - curricular participation	3	5

source: felder, et al., \a study of student performance in an introductory chemical engineering course,\ 1992 asee annual conference proceedings, pp. 1516 - 1519.
what is the expected count of students with high extracurricular participation and good grades?
a. 8
b. 112
c. 5.86
d. 3

Explanation:

Step1: Calculate row and column totals

Row - total for high extracurricular participation: $3 + 5=8$
Column - total for good grades: $11 + 68+3 = 82$
Grand - total of students: $112$

Step2: Use the formula for expected count

The formula for the expected count in a contingency - table is $E=\frac{(\text{row total})\times(\text{column total})}{\text{grand total}}$.
$E=\frac{8\times82}{112}=\frac{656}{112}\approx5.86$

Answer:

C. 5.86