Question

A college professor is curious if location of seat in class affects grade in the class. They are teaching in a lecture hall to 200 students. The lecture hall has 10 rows, so they split the rows into 5 sections – Rows 1-2, Rows 3-4, Rows 5-6, Rows 7-8, and Rows 9-10. At the end of the course they determine the top 25% of grades in the class, and if location of seat makes no difference, they would expect that these top 25% of students would be equally dispersed throughout the classroom. Their observations are recorded below. Run a Goodness of Fit test to determine whether or not location has an impact on grade. Let α=0.05.

Hypotheses:

H₀: Location in the classroom does does not impact final grade?

H₁: Location in the classroom does does not impact final grade?

Enter the expected count for each section in the table below.

	Rows 1-2	Rows 3-4	Rows 5-6	Rows 7-8	Rows 9-10
# in Top 25%	12	7	10	8	13
Expected Counts

After running a Goodness of Fit test, does the professor have evidence to conclude that location in the classroom has an impact on final grade?

Yes No

Answer 1

H0: Location in the classroom does not impact final grade

H1: Location in the classroom impacts final grade

	Observed	Expected	(Oi - Ei)^2/Ei
Rows 1-2	12	10	0.4
Rows 3-4	7	10	0.9
Rows 5-6	10	10	0
Rows 7-8	8	10	0.4
Rows 9-10	13	10	0.9
	50		2.6

degrees of freedom, df = 4

Test statistic, chi-square = 2.6

critical value of chi-square = 9.49

As test statistic is less than the critical value, failed to reject the null hypothesis.

Location in the classroom does not impact final grade