A state education department has a list of all 240 public middle schools in the state. Each school has 120 seventh-grade students. The department randomly selected 24 schools from the list and randomly assigned 12 of the selected schools to use a new reading program in all seventh-grade English classes for one year. The other 12 selected schools continued using their usual reading instruction.
At the end of the year, researchers randomly selected 30 seventh-grade students from each selected school to take the same reading assessment. The mean assessment score for sampled students at schools using the new program was 4 points greater than the mean score for sampled students at schools using usual instruction.
Which choice most accurately describes a conclusion supported by this study?
For questions about studies, first identify who was randomly selected; that determines the population to which results may be generalized. Next, identify whether a treatment was randomly assigned; that determines whether a causal conclusion is supported. Finally, reject choices that turn an average group result into a claim about every individual or that extend the conclusion beyond the population actually sampled.
Hints
Separate the two kinds of randomization
Determine what the random selection of schools tells you, and then determine what the random assignment of schools tells you.
Focus on the unit assigned
The treatment was assigned to entire schools. Consider whether random assignment must occur at the individual-student level to compare the two instruction methods fairly.
Check the scope
A supported conclusion should match both the grade level and the type of schools included in the sampling frame.
Desmos Guide
Prioritize study design
Desmos is not needed for this question. Identify the random selection of schools for generalization and the random assignment of schools for causation.
Optional count check
If desired, use the calculator to verify that the researchers assessed students. This calculation does not determine the conclusion; the study’s randomization methods do.
Step-by-step Explanation
Identify the population
The 24 schools were randomly selected from the list of all public middle schools in the state. Also, the same number of seventh-grade students was sampled from each selected school, and each school has the same number of seventh-grade students. Therefore, the intended population is seventh-grade students at public middle schools in the state.
Identify the source of a causal conclusion
The selected schools, rather than individual students, were randomly assigned to use either the new program or usual instruction. Random assignment of schools is still random assignment, so differences in average scores can be attributed to the instruction method.
Avoid claims that are too specific or too broad
The 4-point difference is a difference between group means, not a guarantee for every student. The study also did not include elementary schools, high schools, or private schools.