Question

2017-2018 Goals
49
44
43
42
42
41
40
40
39
39
39
37
36
36
35
35
34
34
34
34

2012-2013 Goals
32
29
28
26
23
23
23
22
22
21
21
21
20
20
20
19
19
18
18
18

2007-2008 Goals
65
52
50
47
43
43
42
41
40
40
38
38
36
36
35
34
34
33
33
32

Given the above three sets of data, we want to compare the three seasons using the ANOVA. Answer the following questions:

1. Using proper notation, write the null and alternative hypothesis statements.

2. In the context of the problem posed, interpret the results of the test and make a conclusion about the hypotheses.

****You must be provide concise explanations in your solutions in order to receive credit****

Answer 1

Given the above three sets of data, we want to compare the three seasons using the ANOVA. Answer the following questions:

1. Using proper notation, write the null and alternative hypothesis statements.
2. Let level of significance = 0.05

Let Group 1= 2017-2018 Goals, Group 2= 2012-2013 Goals, Group 3= 2007-2008 Goals

H₁: At least one of the mean is different from the others

2. In the context of the problem posed, interpret the results of the test and make a conclusion about the hypotheses.

ANOVA test is applied to the data.

Calculated F=63.87, P=0.0000 which is < 0.05 level of significance. Ho is rejected.

We conclude that there is significant difference in average goals among the three seasons.

Excel Addon Megastat used

One factor ANOVA
	Mean	n	Std. Dev
2017-2018 Goals	38.6500	20	4.0817
2012-2013 Goals	22.1500	20	3.8699
2007-2008 Goals	40.6000	20	8.0551
Total	33.8000	60	10.0369
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	4109.7000	2	2054.8500	63.87	0.0000
Error	1833.9000	57	32.1737
Total	5943.6000	59