Question 55·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A school district wanted to evaluate a new reading program. The district randomly selected 160 ninth-grade students from across its schools. The selected students were randomly assigned: 80 to use the new program during English class for one semester and 80 to continue the usual instruction. At the end of the semester, the average standardized reading score for the program group was 5 points higher than for the usual-instruction group, and the difference was statistically significant.
Which choice is the most appropriate conclusion based on this study?
First, identify whether the study used random assignment (supports causation) and random selection (supports generalization to the population sampled). Then check whether the reported difference is statistically significant (reduces the chance explanation). Finally, choose the option that matches both the appropriate causal claim and the correct scope—avoid overgeneralizations and scenarios not described in the study, such as volunteers.
Hints
Look for random assignment
Did the study randomly assign students to the new program or the usual instruction?
Look for random selection
Were the participants randomly selected from a clearly defined population?
Watch the scope of the claim
Be careful about conclusions that go beyond the district or that mention volunteers, which are not part of this design.
Desmos Guide
Create a study-design checklist
Insert a note with two items: Random selection? Random assignment? Mark both as Yes based on the prompt.
Map each answer to the checklist
For each option, ask: (a) Does it claim causation (needs random assignment)? (b) What population does it generalize to (needs random selection)?
Select the supported scope and claim
Use your checklist: with both random selection and random assignment marked Yes, choose the option that makes a causal claim and limits the conclusion to ninth-grade students in this district.
Step-by-step Explanation
Identify study type and assignment
Students were randomly assigned to either the new program or usual instruction, making this a randomized experiment. Random assignment allows a cause-and-effect conclusion if a statistically significant difference is observed.
Check generalizability
Students were randomly selected from the district’s ninth-grade population. Random selection supports generalizing the results to that population (ninth-grade students in this district).
Use significance to rule out chance
The reported difference was statistically significant, making it unlikely to be due to random chance alone. Combined with random assignment, this supports a causal effect.
Match the correct scope and claim
Choose the option that makes a causal claim limited to ninth-grade students in this district: The new reading program caused an increase in reading scores for ninth-grade students in this district.