To judge a study's conclusion, separate random sampling, which sets who the findings can represent, from random assignment, which supports cause. Trace who could be selected and which groups received the treatment, then check whether the result describes an average or each person. Assigning whole groups at random can support a causal claim even if their members weren't assigned one by one.
Hints
- Hint 1
A random sample uses chance to select from a larger group. The department started with a list of public middle schools in the state. Which schools could have been selected, and which types could not?
- Hint 2
A school can be the unit of random assignment: chance picks which schools use the program. Students need not be assigned one by one for the program schools to be compared with the usual-instruction schools.
- Hint 3
The mean is the group average. A difference between two means doesn't tell you how any one student's score changed. Does that group comparison specify a result for every student?
Step-by-step
Check sampling, assignment, and averages
Step 1Find which schools the study can represent
No Desmos needed. The question is about study design, not arithmetic. The department randomly selected schools from its list of all public middle schools in the state. That random sample lets the results speak about the state's public middle schools, but not other types of schools.
- Step 2
Find which students the scores can represent
Researchers randomly selected seventh graders from each selected school to take the assessment. So the scores can represent seventh graders at those schools, not only the students tested. Combined with the school sample, this reaches seventh graders at public middle schools across the state.
- Step 3
Decide whether the comparison supports cause
Schools, not individual students, were randomly assigned: used the new program, and kept their usual instruction. This is an experiment because chance chose which instruction each school received. Preexisting differences between schools weren't used to choose the groups, so the comparison can support a causal conclusion about the program.
- Step 4
Match the conclusion to the measured result
The -point gap is between mean scores. A mean is an average, so that gap doesn't promise a -point gain for each student. The study supports the conclusion that the program increases the average assessment score of seventh graders at public middle schools in the state. Choice C.