True or False: When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.

Verified step by step guidance

1. Understand the concept of cluster sampling: In cluster sampling, the population is divided into groups called clusters, and a sample of these clusters is selected. Then, either all individuals within chosen clusters or a sample of individuals within those clusters are studied.
2. Recall what it means for clusters to be heterogeneous: Heterogeneous clusters contain individuals that are diverse or varied within each cluster, meaning each cluster is somewhat representative of the entire population.
3. Consider the implication of cluster heterogeneity on sampling: If clusters are heterogeneous, each cluster resembles the population, so sampling fewer clusters but more individuals within those clusters can still capture the population's diversity.
4. Contrast this with homogeneous clusters: If clusters were homogeneous (each cluster is similar internally but different from others), it would be better to sample more clusters with fewer individuals to capture the population variability.
5. Therefore, when clusters are heterogeneous, having fewer clusters with more individuals is generally better because each cluster already represents the population well, making the statement True.

Key Concepts

Cluster Sampling

Cluster sampling is a method where the population is divided into groups, or clusters, and a random sample of these clusters is selected. All individuals within chosen clusters are then studied. This technique is often used for practical reasons, such as reducing costs or logistical complexity.

Heterogeneity Within Clusters

Heterogeneity within clusters means that individuals inside each cluster are diverse or varied in characteristics. When clusters are heterogeneous, each cluster can represent the population well, so sampling fewer clusters with more individuals might still capture population variability.

Sampling Efficiency and Bias

Sampling efficiency relates to how well a sample represents the population with minimal error. In cluster sampling, having fewer clusters can increase sampling bias if clusters are homogeneous, but if clusters are heterogeneous, fewer clusters may suffice. Understanding this balance helps in designing effective samples.