Question

Ms. Smith teaches three Algebra 1 classes that cover exactly the same content. She is wondering if changing the order of some of the lessons would be beneficial to students. In class A, she teaches everything in the traditional order. In class B, she decides to skip Chapter 1 as it is preliminary information that students may already know. In class C, she decides to do Chapter 5 prior to doing Chapter 3. She would like to know if there are any significant differences in the average scores of the three classes.

Class A	Class B	Class C
50.90	91.04	58.93
28.55	81.51	40.52
46.33	26.55	43.89
28.42	5.56	47.99
36.19	36.49	22.14
93.61	70.91	40.42
23.73	32.23	33.73
77.83	50.48	60.29
54.34	40.52	75.05
43.32	38.47	37.40
63.96	45.63	70.01
56.19	89.13	31.17
17.70	33.04	13.41
81.86	23.31	10.12
86.10	74.89	62.96
25.61	41.79	89.27
52.89	42.04	44.58
21.31	98.38	4.75
41.44	76.79	34.15
99.71	20.96	5.06
74.50	18.66	85.20
92.45	82.75	20.23
98.38	55.04	56.49
4.10	13.89	31.12
34.47	49.37	17.87

Answer 1

Since we need to compare more than two population means so one way ANOVA will be used.

Following is the output of one way ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Class A	25	1333.89	53.3556	788.9803173
Class B	25	1239.43	49.5772	705.9474877
Class C	25	1036.75	41.47	571.4606583
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1843.920715	2	921.9603573	1.338509734	0.268682	3.123907
Within Groups	49593.32312	72	688.7961544
Total	51437.24383	74

The p-value of F test is:

p-value = 0.2687

Since p-value is greater than 0.05 so we cannot conclude that there is a significant differences in the average scores of the three classes.