Explain why cluster sampling is a probability sampling design.

Cluster sampling is a probability sampling design due to the following reasons:

1. Random Selection: In cluster sampling, the selection of groups or clusters is done randomly. This means that every cluster in the population has an equal chance of being selected, which is a fundamental principle of probability sampling.

2. Representativeness: Since clusters are often naturally occurring groups, they tend to be representative of the population. This means that the characteristics of the population are likely to be well represented in the sample, which is another key feature of probability sampling.

3. Efficiency: Cluster sampling can be more efficient than other types of probability sampling. This is because it can be less time-consuming and less costly to sample groups rather than individuals, especially when the population is widely dispersed.

4. Practicality: In some cases, cluster sampling may be the only practical option. For example, if a complete list of individuals in the population is not available, but a list of clusters is, then cluster sampling can be used.

5. Statistical Analysis: The data obtained from cluster sampling can be analyzed using standard statistical methods, which is another characteristic of probability sampling.

In conclusion, cluster sampling is a probability sampling design because it involves random selection, it is representative, efficient, practical, and allows for standard statistical analysis.