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In: Statistics and Probability

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

Solutions

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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