Methods of Sampling and Data Collection in Statistics

Q1)
a) Slovin’s formula
N n n
5% error 1% error
1200 300 1071.42857
500 222.222222 476.190476
1600 320 1379.31034
4200 365.217391 2957.74648
bi) Simple random sampling
Step 1: making a list of all 200 schools in different municipalities
Step 2: assigning a sequential number to each the schools. This will act as sampling frame.
Step 3: figuring out the sample size, the sampling size in this case is 40
Step 4: using a random number generator select the sample using sampling frame from step 2 and step
3
This will mean that using the sample size of 40 and the total number of schools which is 200, we will
generate 40 random numbers between 1 and 200.
Sequential
number
Random
numbers
1 41
2 168
3 109
4 178
5 120
6 122
7 81
8 197
9 85
10 101
11 24
12 4
13 40
14 200
15 168

16 92
17 130
18 132
19 85
20 97
21 9
22 157
23 88
24 77
25 86
26 79
27 156
28 189
29 143
30 93
31 181
32 193
33 113
34 6
35 106
36 160
37 12
38 31
39 144
40 122
ii) Systematic sampling
Step 1: A number will be assign to every element, in this case from 1 to 200
Step 2: Deciding the sample size, in this our sample size is 40
Step 3: Dividing the total population of 200 by the sample size of 40 = 200/40 = 5. This will mean that we
will be choosing every 5th value
Step 4: using the sampling digit in step 3 to a certain point
Sample
points
1 1 2 3 4 5
2 6 7 8 9 10
3 11 12 13 14 15
4 16 17 18 19 20
5 21 22 23 24 25