Q 1.36. - Elementary Statistics

Question

The members of a population are numbered 1-5.

(a) List the 10 possible samples (without replacement) of size 3 from this population.

(b) SRS of size 3 is taken from the population, what are the chances of selecting 1, 3, and 5? Explain your answer.

(c) Use Table I in Appendix A to obtain an SRS of size 3 from the population. Start at the single-digit number in line number 5 and column number 20, read down the column, up the next, and so on.

Step-by-Step Solution

Answer

Part (a) 

S. No.	Samples
1	1, 2, 3
2	1, 2, 4
3	1, 2, 5
4	1, 3, 4
5	1, 3, 5
6	1, 4, 5
7	2, 3, 4
8	2, 3, 5
9	2, 4, 5
10	3, 4, 5

Part (b) 0.1

Part (c) The SRS of size 3 is 1, 4, and 5.

Part (a) Step 1. Given information.

The given statement is:

List the 10 possible samples (without replacement) of size 3 from this population.

Part (a) Step 2. List 10 possible samples of size 3.

The population consists of five numbers:

1, 2, 3, 4 and 5

So, for the given population, the 10 possible samples without replacement of size 3 are shown below:

S. No.	Samples
1	1, 2, 3
2	1, 2, 4
3	1, 2, 5
4	1, 3, 4
5	1, 3, 5
6	1, 4, 5
7	2, 3, 4
8	2, 3, 5
9	2, 4, 5
10	3, 4, 5

Part (b) Step 1. Find the probability of selecting 1, 3, and 5.

We have drawn 10 samples from the given population in part (a).

Every sample has an equal probability of being chosen.

Or, to put it in other words, each sample has a one-in-a-million chance of being chosen.

We can observe that the digits 1, 3, and 5 are only found in one sample.

Probability of selecting a sample with 1, 3, and 5:

$$\begin{gathered} =\frac{1}{10} \\ =0.1 \end{gathered}$$

Part (c) Step 1. Obtain an SRS of size 3 using the table I in appendix A.

• Use table I Random Numbers.
• Choose 5 in Line number
• Then choose 20 in column number
• In line number 5, start with a single-digit number
• then select the first number 5
• Skip 0 and numbers above 5, also avoid duplication of numbers
• After that move down column 20. The next number is 4
• Similarly, continue column 20 down and then column 21 up, the next number is 1.

Therefore, the SRS of size 3 is 1, 4, and 5.