A study performed by a Columbia University professor (described in Report on Business, August 1991) counted the number of times per minute professors from three different departments said ”uh” or “ah” during lectures to fill gaps between words. The data d

A study performed by a Columbia University professor (described in Report on Business, August 1991) counted the number of times per minute professors from three different departments said ”uh” or “ah” during lectures to fill gaps between words. The data derived from observing 100 minutes from each of the three departments were recorded. If we assume that the more frequent use of “uh” and “ah” results in more boring lectures, can we conclude that some departments’ professors were more boring than others?

Let µ1,µ2 and µ3 are the population averages for English, Mathematics and Political Science so here the hypothesis of interest is,

H0: µ1 =µ2= µ3 against Ha: at least one mean is significantly different.

The ANOVA table as obtained from Excel is given below,

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
English	100	581	5.81	6.216
Mathematics	100	530	5.30	4.051
Political Science	100	533	5.33	3.900
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	16.38	2	8.190	1.734	0.178	3.026
Within Groups	1402.5	297	4.722
Total	1418.88	299

Here as the observed F test statistic = 1.734 < Critical F = 3.026 thus we are failing to reject the null hypothesis and concluding at 5% significance level that that some departments’ professors were not more boring than others.

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