2019
Tutorial
Chapter 1
1. The following table gives the price of used-boats and the number of hours it has run.
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Hours
1043
1269
895
986
853
1285
1047
1625
847
1063
1053
952
1149
1300
1000
1678
990
1165
874
960
Price (R1000)
25
30
26
29
28
31
29
30
29
27
27
30
28
28
28
28
28
24
31
26
No
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Hours
1256
1594
1402
852
1282
1245
1323
712
1515
926
917
1019
1427
1451
1401
1358
1442
1337
1264
1250
Price (R1000)
29
24
31
28
23
26
26
29
29
29
29
27
33
26
27
27
26
26
29
28
No
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Hours
1320
851
917
1176
1290
1216
1234
1630
1199
951
948
1507
1540
1157
1177
1259
1183
1118
1610
1661
Price (R1000)
26
29
29
29
29
25
28
27
30
28
26
25
26
28
27
28
29
27
28
26
1.1 Draw a random sample of size 10 from the list, read the random numbers from left to right, beginning at Row 20,
Column 10 on the SECOND page of Table A1 in Appendix A. List the sample of boats and their prices in R1000.
(The sum of all the sample’s prices in R1000 = 270 )
1.2 Draw a systematic sample of size 15 from the list. Let the first randomly chosen element be number 2. List the
sample of boats and the hours it has run. (The sum of the sample’s hours = 17 928 )
2.
The following table gives the ages of people applying for house loans:
Male
Nr
1
2
3
4
5
6
7
Age
40
62
26
60
30
56
50
Nr
8
9
10
11
12
13
14
Age
65
21
23
72
36
47
26
Nr
15
16
17
18
19
20
21
Age
28
60
39
57
31
50
72
Nr
22
23
24
25
26
27
28
Age
63
57
44
21
52
37
27
Nr
29
30
31
32
33
34
35
Age
49
48
32
56
69
56
20
Nr
36
37
38
39
40
41
42
Age
27
38
73
73
58
28
63
Female
Nr
1
2
3
4
5
Age
51
26
59
34
54
Nr
6
7
8
9
10
Age
72
45
22
45
37
Nr
11
12
13
14
15
Age
74
37
47
33
46
Nr
16
17
18
19
20
Age
43
53
39
42
68
Nr
21
22
23
24
25
Age
60
26
33
32
50
Nr
26
27
28
29
30
Age
56
48
21
45
60
Draw a stratified random sample of size 15 from the population.
For the stratum male, read vertically downwards and begin at Row 10, Column 8 on the first page of Table A1 in
Appendix A. (The sum of all the male sample’s ages = 413)
For the stratum female, read vertically downwards and begin at Row 20, Column 18 on the second page of Table A1.
(The sum of all the sample’s ages = 290 )
3. The members of a class are numbered 1 to 485. Use the following random numbers to create a random sample of
6 students. Work from left to right. (The selected random numbers add up to 1723)
1 7 2 5 8 9 4 0 4 6 3 8 7 0 3 3 2 1 2 7 4 3 7 9
7 9 9 6 6 0 1 7 3 5 4 9 3 1 4 9 2 4 0 9 3 5 4 7
5 3 2 2 8 1 5 3 2 1 9 2 1 9 3 3 6 2 5 2 7 3 5 1
4. The houses in a street are numbered from 1 to 55. Use the random numbers in question 3, working from top to
bottom, to select a random sample of 5 houses. (The selected random numbers add up to 113)
5. A biologist plants 150 seeds in pots numbered from 1 to 150. List the numbers of the pots you would include in a
systematic sample of size 10. Let the first number you select be 4.
6. A company places each of its employees on one of 5 salary scales: A, B, C, D and E. The number of employees
on each scale is listed below:
A
130
B
275
C
415
D
260
E
90
How many people from each scale should be included in a sample of size 80?
An old test
1. A campus planner at a local university working on bikeways needs information about bicycle commuters. She
designed a questionnaire. One of the questions asks how many minutes it takes the rider to pedal from home to
campus. Information on 24 bicycle commuters (numbered from 1 to 24) yielded the following times:
No
TIME
No
TIME
No
TIME
No
TIME
No
TIME
No
TIME
1.
22
2.
29
3.
27
4.
30
5.
12
6.
22
7.
22
8.
13
9.
19
10.
23
11.
17
12.
10
13.
9
14.
20
15.
18
16.
13
17.
22
18.
38
19.
13
20.
14
21.
17
22.
10
23.
15
24.
31
Use systematic sampling method to select required sample of 4 bicycle commuters. Let the first element of the sample
be 2.
(3)
2. Answer the following as true or false: (indicate the correct option with X)
(5)
True False
2.1 A parameter is a statistical measure computed from the entire universe
2.2 A variable is a statistical measure computed from a subset taken from the
universe
2.3 A population is always only a collection of people
2.4 When we investigate the whole population it is called a census
2.5 Inferential statistics condenses large volumes of data into few summary
measures.
3. There are 3210 students in 4 different departments K; L; M and N of a faculty in a particular university. A stratified
random sample size of 125 must be drawn from the population. Calculate the number of students chosen from each
department using stratified random sampling method.
(4)
Department
Number of students
K
700
L
555
M
1200
N
755
Sample
4. Suppose there are 192 people on the electoral roll in a retirement village. Select a random sample of 4 people from
the village using the table of random numbers given below. Start at the top left corner and read the random numbers
vertically from top to bottom.
(4)
Row
1
83 20 37 15
22 21 78 47
14 51 94 38
69 47 58 04
29 85 48 58
2
55 06 80 64
71 41 32 97
73 05 04 33
96 16 42 50
91 30 86 66
3
19 54 68 57
27 10 08 16
41 89 75 46
83 12 20 50
03 73 77 24
4
42 49 74 33
24 22 79 32
55 23 63 66
78 83 60 61
73 84 85 52
5
17 87 57 75
31 11 81 00
86 28 26 23
68 11 76 65
64 19 47 83
Questions from 2016 exam papers:
1.1
A politician who is running for the office of mayor of a city with 25 000 registered voters’ commissions a survey.
In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her.
1.1.1 What is the population of interest?
(2)
1.1.2 What is the sample?
(2)
1.2.1 The owner of a large fleet of 350 taxis in Johannesburg is trying to estimate his costs for the next year’s
operations. He needs to select a sample of 20, what sampling method should he use?
(2)
A:
Simple
random
sampling
B:
Random
sampling
C:
Stratified
random
sampling
D:
Snowball
sampling
E:
Quota
1.2.2 Determine the scale of measurement for the following: the total annual fuel costs of each of the 20 taxis.
A:
Nominal
B:
Ordinal
C:
Interval
D:
Ratio
E:
None
Indicate if the following are true or false:
2.1
The number of defective items manufactured, is an example of qualitative data.
(1)
2.2
A population is a subset of a sample on which observations are made.
(1)
2.3
Data which is captured at the point where it is generated is called primary data.
(1)
2.4
Collecting of data, analysis of the data and drawing meaningful conclusions are the three basic statistical
processes that lead to good decision making.
(1)
(2)
2.5
The questionnaire is the only method to collect qualitative data.
(1)
2.6
The number of white cars passing through a tunnel in one hour is an example of quantitative data.
(1)
Questions from 2017 exam papers:
1.1 In order to check public transport busses for roadworthiness, a sample of 35 is required from the population of
1260 registered busses. If you need to draw a systematic sample and the first vehicle you select is bus number 15,
what is the number of the next two busses you must check?
(2)
A:
51 and 87
B:
35 and 70
C:
50 and 85
D:
36 and 72
E:
None
1.2 A big shop has got a fresh produce, clothing and cosmetic department. The manager plans to send 12 of the
consultants on a marketing course. He decides to take a stratified random sample. How many consultants from each
department should he select?
(3)
Department
Consultants
Fresh Produce
25
Clothing
12
Cosmetic
20
Number of consultants
selected for course
2. A group of students is numbered 1 to 250. Use the random number table below and select a sample of 5 students,
starting from row 3 column 11 read the numbers vertically downwards. Write the number of the sampled students in
the cells provided.
(5)
Row
1
2
3
4
5
A:
90 73 51 07 27
67 37 66 97 75
76 19 85 46 62
97 76 37 48 02
55 24 37 37 72
30 68 26 75 42
98 54 02 23 60
46 64 30 58 35
83 03 63 59 78
35 96 54 05 45
B:
33 35 11 88 03
80 96 13 08 79
62 75 25 68 52
55 25 54 22 99
26 00 71 29 15
C:
83 17 00 29 82
28 48 01 72 28
54 64 28 49 57
44 39 35 84 50
03 85 34 15 27
D:
94 50 42 39 61
26 07 95 83 89
66 52 70 54 74
73 51 68 77 81
79 77 49 03 64
E: