QuestionA researcher wants to sample students from a high school.
(a) Describe a simple random sampling plan.
(b) Describe a systematic sampling plan.
(c) Does sampling from each grade create a stratified or cluster sample? Explain.

Studdy Solution
(c) The described sampling plan is an example of a stratified random sample, not a cluster sample.
In a stratified random sample, the population is divided into non-overlapping groups or strata, and a simple random sample is drawn within each group. In this case, the strata are the four grades, and a simple random sample is taken from each grade.
In a cluster sample, the population is divided into groups or clusters, and a random sample of clusters is selected. All individuals within the selected clusters are included in the sample. If the researcher had selected entire grades at random, this would be a cluster sample.
$$\text{Stratified Random Sample} = \text{Simple Random Sample}(\text{Each Grade})$$