Question

National Bearings manufactures bearings at plants located in Portland Oregon, Houston Texas, and Jacksonville Florida. To measure employee knowledge of Total Quality Management (TQM), six employees were randomly selected at each plant and tested. The test scores for these employees are given in DATA. Managers want to know if, on average, knowledge of TQM is equal across the 3 plants. Test equality of mean scores at x = 0.05

Ovservation	Portland	Houston	Jacksonville
1	85	71	64
2	75	75	69
3	82	73	67
4	76	74	74
5	71	69	80
6	85	82	72

A. none of the answers are correct

B. Equality of means is not rejected with pvalue 0.295. Knowledge of TQM is equal across the 3 plants.

C. Equality of means in not rejected with pvalue of 0.060. Knowledge of TQM is equal across the 3 plants.

D. Equality of means is rejected with pvalue 0.010. Knowledge of TQM is not equal across the 3 plants.

E. Equality of means is rejected with pvalue 0.003. Knowledge of TQM is not equal across the 3 plants

Answer 1

Consider

: Average Knowledge of TQM at Portland plant.

: Average Knowledge of TQM at Houston plant.

: Average Knowledge of TQM at Jacksonville plant.

We have to testing the hypothesis

Whether or not Average Knowledge of TQM is equal across the plants ?

i.e Null Hypothesis -

against

Alternative Hypothesis- Ha : Knowledge of TQM is not equal across the 3 plants.

By using Excel

Observation	Portland	Houston	Jacksonville
1	85	71	64		Anova: Single Factor
2	75	75	69
3	82	73	67		SUMMARY
4	76	74	74		Groups	Count	Sum	Average	Variance
5	81	69	80		Column 1	6	484	80.66667	18.66667
6	85	82	72		Column 2	6	444	74	20
					Column 3	6	426	71	32
					ANOVA
					Source of Variation	SS	df	MS	F	P-value	F crit
					Between Groups	293.7778	2	146.8889	6.235849	0.010692	3.68232
					Within Groups	353.3333	15	23.55556
					Total	647.1111	17

Alpha : level of significance = 0.05

From excel output p-value = 0.01062

Since p-value < level of significance alpha.

We reject the null Hypothesis at 5% level of significance.

Correct Answer : D - Equality of means is rejected with p-value 0.010. Knowledge of TQM is not equal across the 3 plants.