Question

Parametirc test or not:

Test statistic:

p-value:

decision:
Is There A Difference Between the Means?

6.7 6.2 3.1 3

10.3 10 5 5.5

6.9 5.5 3.3 3.1

10.5 6.3 4.3 5.4

4.5 4.6 1.8 2

5.6 5.6 2 2.6

5.9 6.1 2.1 2.5

8 11.7 4 4.6

8 7.4 3.3 3.1

5.8 5.2 3.1 2.9

6 7.3 3.0 3.2

8.7 5.3 2.7 3

6 5.5 2.1 2.2

7.2 6.3 3.5 3.2

5.9 4.6 2.9 3.4

6 7.4 3 3.3

7.2 7.8 3.7 3.4

8.6 9.4 5.1 5.7

7.2 8.1 2.8 3.1

5.8 5.4 2.2 1.8

3.3 4 1.7 1.8

6.8 5.1 2 1.8

3.7 3.5 2.2 2.1

12 10.8 5.7 5.8

9.5 6.9 4.4 3.2

21.4 15.4 7.2 6.9

6.5 7 3.5 3

4.6 6.4 3.2 2.7

3.9 4.2 2.9 2.4

4.6 3.6 1.4 1.7

9.1 11.2 4.5 5.1

3.3 3 1.7 1.5

8 7.7 4 3.6

15.3 15.2 12 6.1

6.8 5.6 3.3 2.6

10.5 7.4 5.8 3.9

5.2 4.2 1.8 2.6

7.2 5.5 2.8 2.7

14.2 12.4 7.6 5.3

11.7 11.4 6.8 6.2

8 8.2 4.9 4.1

10 10 4.7 5.3

6.1 9.7 1.9 2.3

4.5 5.1 2.6 2.3

4 3.4 2 1.9

12.9 10 4.4 4

6.5 7.5 3.5 2.3

17.3 7.9 6.4 8.1

Answer 1

We will assume parametric setup for this problem

Here we will use ANOVA test to check whether the means are different.

that is to test,

H0: means of all 4 groups are same

vs

H1: at least 2 groups are different means

To test this we will use Excel software and the output is

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	48	377.7	7.86875	13.6255984
Column 2	48	348	7.25	8.538297872
Column 3	48	177.9	3.70625	3.821449468
Column 4	48	168.3	3.50625	2.384428191
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	760.2539	3	253.418	35.73069977	2.54521E-18	2.652645615
Within Groups	1333.379	188	7.092443
Total	2093.633	191

Test statistic: F=35.73069977

p-value: 0.00000

decision: we will reject H0 and claim that groups has significantly different means.
Is There A Difference Between the Means?

YES. There is significant difference in means.