Question

Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift. At the 0.05 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?

	Units Produced
Employee	Day	Afternoon	Night
Skaff	31	38	34
Lum	37	35	39
Clark	38	27	37
Treece	35	28	26
Morgan	22	21	21

1. What is your decision regarding H₀? (Round your answers to 2 decimal places.)

Answer 1

Step.1 Enter data in excel sheet.

Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 'ANOVA : Two Factor without replication'.

Step.3 New window pop-up on screen. Provide input and output range.

Excel output:

Employee	Day	Afternoon	Night		Anova: Two-Factor Without Replication
Skaff	31	38	34
Lum	37	35	39		SUMMARY	Count	Sum	Average	Variance
Clark	38	27	37		Skaff	3	103	34.33333	12.33333
Treece	35	28	26		Lum	3	111	37	4
Morgan	22	21	21		Clark	3	102	34	37
					Treece	3	89	29.66667	22.33333
					Morgan	3	64	21.33333	0.333333
					Day	5	163	32.6	42.3
					Afternoon	5	149	29.8	45.7
					Night	5	157	31.4	58.3
					ANOVA
					Source of Variation	SS	df	MS	F	P-value	F crit
					Rows	452.9333	4	113.2333	6.84879	0.010689	3.837853
					Columns	19.73333	2	9.866667	0.596774	0.57336	4.45897
					Error	132.2667	8	16.53333
					Total	604.9333	14

Test statistic, for employee F= 6.85  and p-value = 0.01

Since p-value is less than 0.05 we reject null hypothesis that mean production rate by employee is same.

Test statistic, for shif F= 0.596 and p-value = 0.57

Since p-value is greater than 0.05 we accept null hypothesis that mean production rate by shift is same.