Question

1. Assume that 3 different service stations were evaluated for overall quality and efficiency by 4 different evaluators (also called “raters”), and the results were as follows:

Rater            Station A             Station B               Station C

I                        72                           72                          75

II                      73                           74                          78

III                     71                           75                          79                                  

IV                     76                           75                          80

Use the .05 level of significance, determine if there is a significant difference in the AVERAGE quality and effectiveness of the stations.

ROUND ALL CALCULATIONS TO 2 DECIMAL PLACES!

Answer 1

Hypothesis:

H0: μ1 = μ2 = μ3

Ha: not all μ's are same

Test:

Excel > Data > Data Analysis > Anova: Single Factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Station A	4	292	73	4.67
Station B	4	296	74	2.00
Station C	4	312	78	4.67
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	56	2	28.00	7.41	0.01	4.26
Within Groups	34	9	3.78
Total	90	11

F stat = 7.41

P value :

P value = 0.01

P value < 0.05, Reject H0

Conclusion:

There is enough evidence to conclude that  there is a significant difference in the AVERAGE quality and effectiveness of the stations.