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.

The given statement is:

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

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:

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:

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

• 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.