Question

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 H₀/H₁ 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

Answer 1

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:

$\\ H_0 : \mu_1 = \mu_2 = \mu_3 \\ \\ H_1 : At \ least \ one \ mean \ is \ different \ than \ others$

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.