91Ó°ÊÓ

The given statement is:

The members of a population have been numbered 1-50.

A sample of size 20 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1-10,

cluster #2 consists of the members of the population numbered 11-20, and so forth.

To obtain a sample of size 20, use the cluster sampling approach.

• The population is separated into clusters in the first step. As we know that the population ranges from 1 to 50 people. It is also assumed that the clusters are 10 clusters in size.
• As a result, there are 5 clusters $\left(=\frac{50}{10}\right)$.
• Thus, cluster 1 has members ranging from 1 to 10,
• cluster 2 has members ranging from 11 to 20,
• cluster 3 has members ranging from 21 to 30,
• cluster 4 has members ranging from 31 to 40, and
• cluster 5 has members ranging from 41 to 50.

• Now Select a small sample of clusters at random.

Each cluster comprises ten members, requiring a sample size of 20.

Thus, 2 $\left(=\frac{20}{10}\right)$clusters are chosen at random from a total of 5 clusters.

Procedure for MINITAB:

Step 1: Select Calc > Random Data > Integer from the menu bar.

Step 2: Double your selected sample size in the Number of rows of data to generate a section, just in case there are repeats. Enter 2 as the sample size.

Step 3: In the Store in the column, type Cluster in column C1.

Step 4: Enter 1 for the minimum value and 5 for the maximum value.

Step 5: Select OK.

MINITAB output: Cluster 1 4

As a result, two clusters have been chosen: 1 and 4

Clusters 1 and 4 are chosen in this case. Members 1 to 10 and 31 to 40 are thus included in the sample.

Members 1-10 and 31--40 make up the sample of 20 members utilizing cluster sampling.

Clusters 1 and 3 are chosen in this case.

Members 1 to 10 and members 21 to 30 make up the sample.

Members 1-10 and 21- 30 make up the sample of 20 members utilizing cluster sampling.