To investigate if standing up while studying affects performance in an algebra class, a teacher assigns half of the $30$students in his class to stand up while studying and assigns the other half to not stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. The teacher does the same for the next two highest-scoring students and continues in this manner until each student is assigned a treatment.

Which of the following best describes this plan?

a. This is an observational study.

b. This is an experiment with blocking.

c. This is a completely randomized experiment.

d. This is a stratified random sample.

e. This is a cluster sample.

We are given an experiment in which a teacher assigns half of the $30$students in his class to stand up while studying and assigns the other half to not stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. We need to find out plan that describes the experiment best from given options.

Each block contains two students, with the first block containing the two highest-scoring students, the second block containing the next two highest-scoring students, and so on. Because kids with similar scores are grouped in a block together, we know these are blocks and not clusters. We also know they're blocks because each block's two pupils are assigned to opposite therapies at random. Blocks must be divided proportionally to the number of treatments and assigned to various treatment groups at random. Experiment totally defines the theory of experiment with blocking. As a result, option (b) is correct option.