Question:
Problem 11.13: A management consulting company presents a 3 - day seminar on project management to various clients. The seminar is basically the same each time it is given. However, sometimes it is presented to high-level managers, sometimes to midlevel managers, and sometimes to low-level managers. The seminar facilitators believe evaluations of the seminar may vary with the audience. Suppose the following data are some randomly selected evaluation scores from different levels of managers after they attended the seminar. The ratings are on a scale from 1 to 10, with 10 being the highest. Use a one-way ANOVA to determine whether there is a significant difference in the evaluations according to manager level. Assume alpha = .05.

Given:

HIGH LEVEL MIDLEVEL LOW LEVEL     7 8 5     7 9 6     8 8 5     7 10 7     9 9 4     10 8       8   TOTAL(rows): 38 62 35 135 n 5 7 6 N =18 7.6 8.86 5.83 7.5

Manual Solutions:

ANOVA - Analysis of Variance

Ho:
Ha: At least one of the means is different from the others

Partition the total variance of the data into 2 variances:
a. Variance resulting from the treatment
b. Error variance, portion of the total variance unexplained by the treatment.

SST = SSC + SSE
(total sum of squares) = (treatment sum of squares) + (error sum of squares)

SSC =

SSC =

SSC = 29.7306

SSE =

SSE = 18.8906

SST =

SST = 48.5

dfc = C -1
dfc = 3 -1 = 2

dfe = N - C
dfe = 18 -3 = 15

MSC = SSC / dfc

MSC = 29.7306 / 2

MSC = 14.8653
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MSE = SSE / dfe

MSE = 18.8906 / 15

MSE = 1.259373333

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Computed F = MSC / MSE

F = 14.8653 / 1.259373333

Computed F = 11.80372778

F table A.7 value = F.05,2,15 = 3.68

GRAPH:

Answer:

Computed f value of 11.80 is greater than table f value of 3.68, therefore we reject the null hypothesis. Not all means are equal. There is a significant difference in the evaluations depending on the manager levels.

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