Question

Dr. Smith believes that there may be a difference in grades based on if the student is a senior, junior, sophomore, or freshman. The results are shown in Table 2. Are Dr. Smith’s grade unequally distributed across grade levels?

Table 2: Dr. Smith’s Grade Distribution by Grade Level
Grade	Senior	Junior	Sophomore	Freshman	Total
A	10	7	1	1
B	20	20	2	2
C	3	3	4	4
D	1	2	8	1
F	1	3	3	4
Total

1A.Conduct a chi-square test at the α = .05 level (the table provided below is to help in your analysis).

1B Do you reject or retain the null hypothesis? Why?

Answer 1

	senior	junior	sophomore	freshman
A	10 ( 6.65)	7 (6.65)	1 (3.42)	1 (2.28)	19
B	20 (15.40)	20 (15.40)	2 (7.92)	2 (5.28)	44
C	3 (4.9)	3 (4.9)	4 (2.52)	4 (1.68)	14
D	1 (4.2)	2 (4.2)	8 (2.16)	1 (1.44)	12
F	1 (3.85)	3 (3.85)	3 (1.98)	4 (1.32)	11
	35	35	18	12	total= 100

expected frequency in (i,j) cell = Rowsum_{i}*Columnsum_{j} / total

Expected freq is written in brackets .