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 0.01 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?

Skaff 37 27 34

Lum 35 26 38

Clark 24 23 22

Treece 22 20 25

Morgan 30 26 37

Answer 1

Ho: µ1=µ2=µ3 = µ4 =µ5

H1: At least two means are not equal

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
skaff	3	98	32.66667	26.33333
lum	3	99	33	39
clark	3	69	23	1
treece	3	67	22.33333	6.333333
morgan	3	93	31	31
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	336.2667	4	84.06667	4.0547	0.033036	5.994339
Within Groups	207.3333	10	20.73333
Total	543.6	14

F stat = 4.0547

F critical = 5.94

F stat < f critical, so do not reject Ho

there is no difference in the mean production rate by shift or by employee

...................

Please revert back in case of any doubt.

Please upvote. Thanks in advance.