A manager wishes to determine whether the mean times required to complete a certain task differ...

A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 10 employees with each of the three levels of training (Beginner, Intermediate and Advanced). Do the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training? Carry our ANOVA test at α 0.05. The data is summarized in the table. Level of Training Number of Employees Average time to finish task Average time Standard deviations Advanced 10 24.2 21.54 Intermediate 10 27.1 18.64 Beginner 10 30.2 17.76

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Expert Solution

here we use F-test using one-way anova with

null hypothesis H0:advanced=Intermediate=beginner

alternate hypothesis Ha: atleast one is different from others

since critical F(0.05,3,27)=3.35 is more than calculated F=0.24, so we fail to reject H0(or accept H0) and conclude that the mean times required to complete a certain task don't differ for the three levels of employee training.

following information has been generated using ms-excel

					within SS		between SS
Group	nj	mean(xj-)	s2	nj*xj-	(n-1)s2	(xj--x-)	nj(xj--x-)2
advanced	10	24.2	463.9716	242	4175.7444	-2.96667	88.0111111
Intermediate	10	27.1	347.4496	271	3127.0464	-0.06667	0.04444444
Beginner	10	30.2	315.4176	302	2838.7584	3.033333	92.0111111


sum	30	81.5	1126.839	815	10141.5492	-3.6E-15	180.066667
grand mean(x-)	27.16667



		ANOVA
SOURCE	DF	SS	MS	F	CRITICAL F(0.05)	p-value
BETWEEN	2	180.07	90.03333	0.24	3.35	0.7885
WITHIN(ERROR)	27	10141.55	375.6129
TOTAL	29	10321.62

orchestra answered 1 year ago

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