UNIVERSITY OF MALTA
ISLANDS AND SMALL STATES STUDIES
SEPTEMBER 2010 EXAMINATION
Date: Monday 6th Sep 2010
Time: 10.30 – 11.30
Unit Code: ISS-5101
Unit Title: Research Methodology
Answer any two questions
(All questions carry 50 marks. Use a separate booklet for each question.)
1. The following table presents data that pertains to a sample of households, relating to
the relationship between income tax and household income per week. What conclusions
can you derive from the data?
Income €
100
210
320
450
490
510
Income Tax €
2
12
30
60
70
90
2. A political analyst was conducting an opinion survey among voters in five districts.
For this purpose he took a random sample of 200 voters from the electoral register, and
classified them by district as follows:
District
Number in sample
Number of voters
1
33
2
42
3
28
4
60
5
37
7000
8000
6000
11000
8000
Does the sample distribution differ significantly from the true number of voters in terms
of districts? Briefly comment on your results, referring to the need for having a
representative sample when conducting opinion polls.
3. Describe and discuss how you would go about writing a dissertation on a theme of
your choice.
4. Briefly distinguish between quantitative and qualitative data using examples of your
choice. Describe the main use and statistical information which can be derived from the
following
a) Histogram
b) Box-plots
1
c) Scatter plots.
5. It is often said that quantitative research involves looking at the spread (distribution) of
a relatively few variables among a general population, while qualitative is the study of
the interrelations between a relatively large number of variables among a select group.
Discuss.
2
REGRESSION FORMULAE
Equation to be estimated
Y = a0 + a1 X + u
a1 = Σxy / Σx2
where x = (X - ̅X̅ ) and y = (Y - ̅Y̅ )
a0 =
̅Y̅ - a1 ̅X̅
R2 = [Σ xy/ √ (Σy2 ΣX2) ]2
or
R2 = a1Σ xy/Σy2
3
Table of the Table of the χ2 Distribution
Right tail areas for the Chi-square Distribution
DF
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1.00
0.00
0.01
0.07
0.21
0.41
0.68
0.99
1.34
1.73
2.16
2.60
3.07
3.57
4.07
4.60
5.14
5.70
6.26
6.84
7.43
8.03
8.64
9.26
9.89
10.52
11.16
11.81
12.46
13.12
13.79
0.99
0.98
0.95
0.90
0.75
0.50
0.25
0.10
0.05
0.03
0.01
0.01
0.00
0.02
0.11
0.30
0.55
0.87
1.24
1.65
2.09
2.56
3.05
3.57
4.11
4.66
5.23
5.81
6.41
7.01
7.63
8.26
8.90
9.54
10.20
10.86
11.52
12.20
12.88
13.56
14.26
14.95
0.00
0.05
0.22
0.48
0.83
1.24
1.69
2.18
2.70
3.25
3.82
4.40
5.01
5.63
6.26
6.91
7.56
8.23
8.91
9.59
10.28
10.98
11.69
12.40
13.12
13.84
14.57
15.31
16.05
16.79
0.00
0.10
0.35
0.71
1.15
1.64
2.17
2.73
3.33
3.94
4.57
5.23
5.89
6.57
7.26
7.96
8.67
9.39
10.12
10.85
11.59
12.34
13.09
13.85
14.61
15.38
16.15
16.93
17.71
18.49
0.02
0.21
0.58
1.06
1.61
2.20
2.83
3.49
4.17
4.87
5.58
6.30
7.04
7.79
8.55
9.31
10.09
10.86
11.65
12.44
13.24
14.04
14.85
15.66
16.47
17.29
18.11
18.94
19.77
20.60
0.10
0.58
1.21
1.92
2.67
3.45
4.25
5.07
5.90
6.74
7.58
8.44
9.30
10.17
11.04
11.91
12.79
13.68
14.56
15.45
16.34
17.24
18.14
19.04
19.94
20.84
21.75
22.66
23.57
24.48
0.45
1.39
2.37
3.36
4.35
5.35
6.35
7.34
8.34
9.34
10.34
11.34
12.34
13.34
14.34
15.34
16.34
17.34
18.34
19.34
20.34
21.34
22.34
23.34
24.34
25.34
26.34
27.34
28.34
29.34
1.32
2.77
4.11
5.39
6.63
7.84
9.04
10.22
11.39
12.55
13.70
14.85
15.98
17.12
18.25
19.37
20.49
21.60
22.72
23.83
24.93
26.04
27.14
28.24
29.34
30.43
31.53
32.62
33.71
34.80
2.71
4.61
6.25
7.78
9.24
10.64
12.02
13.36
14.68
15.99
17.28
18.55
19.81
21.06
22.31
23.54
24.77
25.99
27.20
28.41
29.62
30.81
32.01
33.20
34.38
35.56
36.74
37.92
39.09
40.26
3.84
5.99
7.81
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
21.03
22.36
23.68
25.00
26.30
27.59
28.87
30.14
31.41
32.67
33.92
35.17
36.42
37.65
38.89
40.11
41.34
42.56
43.77
5.02
7.38
9.35
11.14
12.83
14.45
16.01
17.53
19.02
20.48
21.92
23.34
24.74
26.12
27.49
28.85
30.19
31.53
32.85
34.17
35.48
36.78
38.08
39.36
40.65
41.92
43.19
44.46
45.72
46.98
6.63
9.21
11.34
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.72
26.22
27.69
29.14
30.58
32.00
33.41
34.81
36.19
37.57
38.93
40.29
41.64
42.98
44.31
45.64
46.96
48.28
49.59
50.89
7.88
10.60
12.84
14.86
16.75
18.55
20.28
21.95
23.59
25.19
26.76
28.30
29.82
31.32
32.80
34.27
35.72
37.16
38.58
40.00
41.40
42.80
44.18
45.56
46.93
48.29
49.64
50.99
52.34
53.67
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