A study asking whether something caused a difference calls for two separate checks. Random sampling tells you whom the results can describe; how people got into the comparison groups tells you whether the study can show cause. Check when chance entered: picking students for a study isn't the same as deciding who gets a pass. A difference between group averages alone doesn't tell you what produced it.
Hints
- Hint 1
A random sample uses chance to choose people from a full list, so it can help describe that whole list. What group is on the roster from which the researchers picked the students?
- Hint 2
To claim cause, look for random assignment: chance must decide who gets the pass, not only who enters the study. Did the researchers give out passes, or did they check records to see who already had them?
- Hint 3
A mean is an average, so a higher mean doesn't say every student attended more school. What group-level comparison do the two averages show?
Step-by-step
Separate random sampling from random assignment
Step 1Find whom the sample can represent
No Desmos needed. This asks what the study design supports, not for a calculation. The researchers picked students at random from the complete district roster. That makes them a random sample, chosen by chance, so the finding can speak about 11th-grade students in the district, not only the students selected.
- Step 2
Check who decided which students got passes
The researchers found in the records that selected students had received passes; they didn't assign passes by chance. This is an observational study: the researchers compared groups that already existed. Random selection helps a finding speak for a population; random assignment helps establish cause. Without assignment, other differences between the groups, such as their commutes, might also affect attendance.
- Step 3
State the conclusion without claiming cause
The pass group had higher mean attendance, meaning a higher average number of days attended per week. So the study supports a district-wide association, or relationship, between receiving a pass and higher mean attendance. It doesn't establish that the passes caused the difference. Choice D.