In a randomized experiment, chance can do two different jobs: random selection tells you who the result can describe, while random assignment helps establish whether the program caused a difference. Compare the groups’ average scores, then keep the conclusion within the population sampled. A difference in averages doesn’t mean every student improved.
Hints
- Hint 1
A random sample is chosen by chance from a larger group. These students were selected from the district’s ninth graders. Which students could that sample represent, and which grades weren’t included?
- Hint 2
In random assignment, chance decides who receives the program instead of letting students choose. Both groups came from the same selected students. Why does that matter when you compare their scores?
- Hint 3
A statistically significant difference would be unlikely from chance alone if the program had no effect. The reported score is an average. Does it tell you what happened to every individual student?
Step-by-step
Check the sample, then the assignment
Step 1Set the population the result can describe
No Desmos needed. This decision depends on how students were chosen and grouped, not on arithmetic. The district chose a random sample of ninth graders across its schools, so the result can represent ninth-grade students in this district, not students in other grades or districts.
- Step 2
Decide whether the comparison supports cause
The selected students were randomly assigned to the program or usual instruction. In random assignment, chance forms the groups rather than students choosing for themselves. That makes preexisting differences unlikely to consistently favor one group; usual instruction gives a baseline for comparison. Random selection sets who the result can speak for; random assignment supports a causal claim.
- Step 3
Match the conclusion to the result
The program group’s average score was 5 points higher. Statistically significant means a gap that large would be unlikely from chance alone if the program had no effect. So the study supports the conclusion that the program caused an increase in average reading scores for ninth-grade students in this district, not that every student improved. Choice A.