For a study asking which conclusion is supported, keep random sampling and random assignment separate. Sampling tells you who the result can represent; assignment tells you whether a difference supports a causal claim. Check whether the finding is about an average rather than every person. A small -value strengthens the evidence of a difference, but it does not expand the population studied.
Hints
- Hint 1
A simple random sample uses chance to select people from a defined population. Only people on the city’s census records could be picked here. How far beyond the sampled adults can that result reasonably reach?
- Hint 2
In random assignment, chance decides who gets each treatment after participants are selected. That helps separate the treatment’s effect from other differences between people. Did the adults choose whether to drink water, or did chance put them in groups?
- Hint 3
A mean is an average. A lower mean with gives evidence about average calorie intake, not a promise that every person who drinks water eats less. Which conclusion respects both the finding and the population sampled?
Step-by-step
Check the sample, assignment, and result
Step 1Set the population limit
No Desmos needed. This asks how the study was run, not for a number to calculate. The researchers used a simple random sample: chance selected the adults from one city’s census records. So the result can speak for adults in that city, but not adults nationwide.
- Step 2
Decide whether the study supports cause
The researchers randomly assigned adults to drink water or nothing before breakfast. Chance, not the adults’ habits, picked their groups. That makes this a randomized experiment: the assigned treatment can explain a difference between the groups. Random assignment supports cause; random sampling sets the population. Don’t stop at association because the result came from a sample.
- Step 3
Match the finding to the conclusion
The water group’s mean, or average, calorie intake was lower. With , the difference is statistically significant: one at least this large would be unlikely if water had no effect. So the study supports water before breakfast causing lower average calorie intake for adults in the city, not a promise about every adult. Choice D.