Three universities had decided to administer the same comprehensive examination
ID: 3179591 • Letter: T
Question
Three universities had decided to administer the same comprehensive examination to the recipients of MBA
degrees. From each university, a random sample of MBA recipients was selected and given the test.
The following table shows the scores taken from samples of students from each university.
Northern University Central University Southern University
75 87 85
80 89 83
84 86 84
85 88 79
81 85 83
Excel was used to run an ANOVA test on this data. The results are below:
SUMMARY
Groups Count Sum Average Variance
Northern 5 405 81 15.5
Central 5 435 87 2.5
Southern 5 414 82.8 5.2
ANOVA
Source of Variation
SS df MS F P-value F crit
Between Groups 94.8 2 47.4 6.12931 0.014652 3.885294
Within Groups 92.8 12 7.733333
Total 187.6 14
State the null and alternative hypotheses and run the test using the output above. What is your conclusion?
Using Fisher’s LSD, find where there are significant differences and draw a final conclusion. Show all your work! Thoroughly interpret your results.
Explanation / Answer
Below are the null and alternate hypothesis
H0: mu1 = mu2 = mu3
H1: at least one mean is different
As we see F-value is greater than the F critical value, this means it lies in rejection region. Hence we reject the null hypothesis.
This means at least one mean is different.
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