Question

A college professor is curious if the location of a seat in class affects grades in the class. They are teaching in a lecture hall with 240 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 the location of the 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 the grade. Let α=0.05. 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 and what is the p-value?

	Rows 1-2	Rows 3-4	Rows 5-6	Rows 7-8	Rows 9-10
# in Top 25%	14	8	13	10	15
Expected Counts	12	12	12	12	12

• A.

  no, the p-value = 0.413907

• B.

  yes, the p-value = 0.586093

• C.

  no, the p-value = 0.58609

• D.

  yes, the p-value = 0.413907

Answer 1

Null hypothesis:

The ratio is equal for all rows ( no impact )

Alternate hypothesis : At least one is different

Event	Observed Frequency(O)	Expected Probability	Expected Frequency ( E)	( O-E)^2	( O-E)^2/E
1-2	14	0.2	12	4	0.333333
3-4	8	0.2	12	16	1.333333
5-6	13	0.2	12	1	0.083333
7-8	10	0.2	12	4	0.333333
9-10	15	0.2	12	9	0.75
Total.	60	60	60		2.833333

The corresponding p value 0.586093

We reject null hypothesis if p < alpha ( 0.05 )

here, p > alpha ( we do not reject the null hypothesis )

All there proportions are same'

no, the p-value = 0.58609