Page 151 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes Random Sampling

Simple random sample is a process in which every item of the population has an equal probability
of being chosen.
There are two methods used in the random sampling:

(1) Lottery method
(2) Using random number table.
(1) Lottery method: Take a population containing four departmental stores: A, B, C and D.
Suppose we need to pick a sample of two stores from the population using a simple
random procedure. We write down all possible samples of two. Six different combinations,
each containing two stores from the population, are AB, AD, AC, BC, BD, CD. We can now
write down six sample combination on six identical pieces of paper, fold the piece of paper
so that they cannot be distinguished. Put them in a box. Mix them and pull one at random.
This procedure is the lottery method of making a random selection.
(2) Using random number table: A random number table consists of a group of digits that are
arranged in random order, i.e., any row, column, or diagonal in such a table contains
digits that are not in any systematic order. There are three tables for random numbers
(a) Tippet’s table (b) Fisher and Yate’s table (c) Kendall and Raington table.
The table for random number is as follows:

40743 39672
80833 18496
10743 39431
88103 23016
53946 43761
31230 41212
24323 18054

Example: Taking the earlier example of stores. We first number the stores.
1 A 2 B 3 C 4 D
The stores A, B, C and D have been numbered as 1, 2, 3 and 4.

We proceed as follows, in order to select two shops out of four randomly:
Suppose, we start with the second row in the first column of the table and decide to read
diagonally. The starting digit is 8. There are no departmental stores with the number 8 in the
population. There are only four stores. Move to the next digit on the diagonal, which is 0. Ignore
it, since it does not correspond to any of the stores in the population. The next digit on the
diagonal is 1 which corresponds to store A. Pick A and proceed until we get two samples. In this
case, the two departmental stores are 1 and 4. The sample derived from this consists of departmental
stores A and D.
In random sampling, there are two possibilities (1) Equal probability (2) Varying probability.

Equal Probability

This is also called as the random sampling with replacement.

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