Question

Four groups of student were chosen and exposed to different methods of teaching. At the end of the period, they were given a test to evaluate the effectiveness of the teaching method.The number os student in each group differed according to group.Using the following mark data, calculate the mean squares between methods. Mean squares between students and the total on overall marks.

G1	G2	G3	G4
65	75	59	94
87	69	78	89
73	83	67	80
79	81	62	88
81	72	83
69	79	76
	90

Answer 1

Here we have data:

G1	G2	G3	G4
65	75	59	94
87	69	78	89
73	83	67	80
79	81	62	88
81	72	83
69	79	76
	90

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	6	454	75.6667	66.6667
Column 2	7	549	78.4286	50.6190
Column 3	6	425	70.8333	91.7667
Column 4	4	351	87.75	33.5833
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	712.5864	3	237.5288	3.77	0.0280	3.127
Within Groups	1196.6310	19	62.9806
Total	1909.2174	22

Hypothesis:

H_o; μ₁ = μ₂ = μ₃ = μ₄

H_a; At least one mean is difference from others.

Test statistics:

F = 3.77

Critical value = 3.127

P-value = 0.0280

Reject the null hypothesis

Here we have sufficient evidence to reject the null hypothesis, critical value is less than test statistics.

We can say that teaching method is effective and all the mean value of the group is not same.