UNIVERSITY OF MALTA
ISLANDS AND SMALL STATES STUDIES
SEPTEMBER 2011 EXAMINATION
Date: Monday 5th 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.)
Answer either question 1 or question 2
Either
Question 1
A researcher tried to test whether the adult males in England are taller than adult men in
Malta. He took a random sample of 300 adult males in the UK and 100 adult males in
Malta. He found that on average Maltese males were 163 cm tall, with a standard
deviation of 6 cm whereas in England the average recorded height was 170 cm with a
standard deviation of 8 cm.
(a) Conduct a test to establish whether there is a statistically significant difference in the
average height of Maltese males compared to English males, with 95% probability.
(b) Would the results of question (a) have been different had the sample sizes been half
those taken in Malta and Gozo? Why?
(c) Would the results of question (a) have been different had the standard deviations been
twice those found in Malta and England? Why?
Or
Question 2
A political analyst wanted to assess whether the sample he obtained was sufficiently
representative of the age groups of potential voters. According to the electoral register,
the proportions of voters by age group are shown in the column headed "voting
population", whereas the sample distribution is that shown in the table headed "sample"
Age Group
Voting Population
Very young (18-25)
40,133
Young (26-32)
35,344
Younger middle-aged (33-45)
60,546
Older middle-age (45-55)
50,123
Older (55-65)
52,453
Old persons (65 and over)
30,004
Total
268,60
Sample
16
15
20
22
19
8
100
(a) Do you consider the sample distribution to be statistically different from that of the
voting population, with a 95% probability
(b) Would your result change if you were to repeat it with a 99% probability?
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(c) Do you think that the political analyst should assess whether his sample is sufficiently
representative of the total voting population, taking into account other characteristics of
the voting population? Which? and why?
Question 3.
(a) What do you understand by a composite index?
(b) Give two examples of composite indices
(c) Show how variables can be rescaled so that an averaging procedure can be carried out
when there are differences in the manner in which the individual components of the index
are measured?
(d) Discuss some strengths and weaknesses of composite indices
Question 4.
(a) Describe, using examples of your choice, some of the main uses of the SPSS
package?
(b) Describe and explain at least two statistical tools, available in the SPSS package,
which can be applied to test for normal distribution.
Question 5
Discuss the relevance of the following terms/notions with respect to qualitative research
methodology and technique: gift exchange; trust; rapport; engaged/engaging; multisensory.
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FORMULAE FOR THE STATISTICAL TESTS
Z test
Z=
X 1 -X 2
√ [(s1 2 / n1) + (s12 / n2)]
where:
s1 and s2 are the standard deviations of the two samples;
X1 and X 2 are the means of the two samples;
n1 and n2 are the sample sizes.
Chi Square Test
χ2 = Σ(oi-ei)2/ei
Where:
oi stands for the observed data of category i
ei stands for the expected data of category i
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4
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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