Are all disciplines in the University equally boring or there are some more boring than others? To answer that question, a study performed at Columbia University counted the number of times per 5-minute interval when professors from three different departments said “uh” or “ah” during lectures to fill gaps between words. These counts were used as a proxy (approximation) for the measure of class boredom. The data from observing one hundred of 5-minute intervals from each of three departments’ professors were recorded in the file below.
- How many populations do we compare?
- What date type is collected?
- What experimental design of the analysis should be applied (independent samples, matched pairs, blocks)?
- What type of test should be applied? Check and report the required conditions for the test if necessary.
- Formulate null/alternative hypotheses H_{0}/H_{1} that need to be tested with these data to find if the departments offer equally boring classes or not.
- Run the test. Report the p-value(s). Use 5% significance level.
- Is there sufficient evidence in the samples collected to conclude that some departments offer more boring lectures than the others?
English | Math | Political Science |
14 | 19 | 14 |
13 | 9 | 5 |
11 | 12 | 4 |
18 | 14 | 18 |
6 | 9 | 17 |
14 | 12 | 16 |
15 | 20 | 12 |
10 | 12 | 9 |
7 | 13 | 13 |
14 | 11 | 20 |
2 | 13 | 22 |
10 | 14 | 16 |
8 | 7 | 10 |
17 | 20 | 16 |
12 | 11 | 17 |
10 | 14 | 16 |
7 | 9 | 9 |
11 | 15 | 5 |
15 | 15 | 9 |
13 | 13 | 14 |
7 | 15 | 6 |
8 | 18 | 14 |
15 | 11 | 16 |
13 | 13 | 11 |
15 | 15 | 19 |
13 | 16 | 10 |
12 | 12 | 17 |
16 | 4 | 6 |
12 | 16 | 12 |
12 | 14 | 17 |
10 | 17 | 17 |
6 | 19 | 8 |
10 | 9 | 11 |
6 | 14 | 5 |
17 | 14 | 10 |
16 | 17 | 15 |
8 | 10 | 12 |
10 | 11 | 15 |
7 | 8 | 11 |
5 | 12 | 9 |
15 | 14 | 14 |
10 | 12 | 14 |
11 | 12 | 7 |
11 | 14 | 16 |
12 | 13 | 18 |
9 | 15 | 11 |
19 | 12 | 16 |
14 | 9 | 12 |
13 | 11 | 12 |
13 | 9 | 15 |
11 | 14 | 16 |
16 | 10 | 14 |
12 | 15 | 14 |
15 | 13 | 20 |
11 | 14 | 17 |
16 | 7 | 18 |
11 | 13 | 16 |
14 | 12 | 19 |
12 | 8 | 13 |
10 | 11 | 13 |
11 | 11 | 22 |
14 | 14 | 8 |
10 | 14 | 13 |
11 | 10 | 21 |
11 | 11 | 13 |
12 | 14 | 12 |
13 | 11 | 21 |
9 | 14 | 8 |
12 | 7 | 10 |
10 | 8 | 15 |
11 | 14 | 8 |
11 | 13 | 17 |
8 | 10 | 14 |
11 | 17 | 10 |
9 | 12 | 16 |
9 | 14 | 14 |
5 | 7 | 14 |
19 | 9 | 15 |
13 | 11 | 12 |
13 | 15 | 12 |
14 | 13 | 17 |
9 | 16 | 21 |
13 | 9 | 16 |
9 | 16 | 18 |
9 | 10 | 11 |
10 | 11 | 13 |
15 | 19 | 11 |
8 | 10 | 14 |
15 | 15 | 19 |
8 | 11 | 17 |
18 | 11 | 13 |
7 | 11 | 12 |
12 | 16 | 10 |
12 | 12 | 13 |
13 | 12 | 13 |
3 | 11 | 15 |
20 | 15 | 9 |
10 | 12 | 14 |
13 | 6 | 10 |
7 | 9 | 6 |
Que.1
We compare 3 populations.
Que.2
Data type is numerical (discrete) .They count the word "uh" and "ah"
Que.3
Experimental design = Block
Que.4
We use one way ANOVA test.
Assumption:
1. Each sample coming from normal population.
2. Samples are independent of each other.
3. Variance of the different samples (block ) should be same.
Que.5
Hypothesis:
Que.6
I used Excel for calculation purpose.
Step.1 Enter data in excel sheet.
Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 'ANOVA : Single Factor'.
Step.3 New window pop-up on screen. Provide input and output range.
Excel output:
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
English | 100 | 1147 | 11.47 | 12.00919 | ||
Math | 100 | 1246 | 12.46 | 9.766061 | ||
Political Science | 100 | 1345 | 13.45 | 16.67424 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 196.02 | 2 | 98.01 | 7.647175 | 0.000578 | 3.026153 |
Within Groups | 3806.5 | 297 | 12.8165 | |||
Total | 4002.52 | 299 |
Test statistic, F = 7.6771
P-value = 0.000578
Since p-value is less than 0.05, we reject null hypothesis at 5% level of significance and conclude that some department offer more boring lectures than others.
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