Question

A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experience workers and the new worker. At the 0.05 significance level, is there any evidence that there is a difference in the amount of work done by the three workers? The following summary of the data is provided. SUMMARY Group Count Sum Average Variance New 5 46 9.2 1.7 A 5 58 11.6 1.3 B 5 59 11.8 1.7 ANOVA Table Source of Variation SS df MS F p-value F critical Between Groups A) B) D) 0.011221 3.885294 Within Groups 18.8 C) E) Total 39.73333 12. Fill in out the blanks A)-E) in ANOVA table. 13. State the null and research hypotheses that are being tested by this procedure. 14. Calculate the test statistic. 15. Identify the distribution of test statistic. 16. What is your decision? 17. Write a complete conclusion based on the ANOVA test.

Answer 1

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
New	5	9.2	1.700	13.889	6.80
A	5	11.6	1.300	2.689	5.20
B	5	11.8	1.700	4.356	6.80
	grand mean=	10.8667		20.933	18.80
				SSTr	SSE

from above:

Source	SS	df	MS	F	p value	F critical
between	20.9333	2.000	10.4667	6.6809	0.0112	3.885294
within	18.8000	12.000	1.5667
total	39.7333	14.0000

13. ) null hypothesis:All three treatments have equal mean

Alternate hypothesis:Not all three treatments have equal mean

14) test statistic =6.6809

15)\ distribution of test statistic =F

16)Decison :Reject Ho

17) we have sufficient evidence to conclude that Not all three treatments have equal mean