Question

define stratified random and cluster sampling. select the statement regarding cluster sampling that is false. a.) the total population is divided into groups. b.) some of the groups are randomly selected. c.) every element of the total population has an equal probability of being selected. d.) every element of some groups is included in the sample.

Answer 1

A stratified sample is obtained by dividing the population into subgroups called strata and then choosing a random sample from each stratum. Cluster sampling involves dividing the population into clusters or groups and randomly selecting some of the clusters to include in the sample.

Step-by-step explanation:

A stratified sample is obtained by dividing the population into subgroups called strata and then choosing a random sample from each stratum. This method is used to ensure that different subgroups are adequately represented in the sample. On the other hand, cluster sampling involves dividing the population into clusters or groups and randomly selecting some of the clusters to include in the sample. All the members of the selected clusters are included in the sample.

Now, let's evaluate the statement options:

1. A. This statement is true. In cluster sampling, the total population is divided into groups or clusters.
2. B. This statement is true. In cluster sampling, some of the groups are randomly selected.
3. C. This statement is false. In cluster sampling, every element of the total population does not have an equal probability of being selected. Instead, only the members of the selected clusters have a probability of being included in the sample.
4. D. This statement is true. In cluster sampling, every element of the selected clusters is included in the sample.

Therefore, the false statement regarding cluster sampling is option C: every element of the total population has an equal probability of being selected.