Question 5·Medium·Evaluate Statistical Claims: Observational Studies and Experiments

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In a 12-week clinical trial, 300 adult volunteers were randomly assigned to one of two groups. The treatment group (150 volunteers) consumed a new vitamin shake each day, while the control group (150 volunteers) did not. At the end of the trial, 18 volunteers in the treatment group and 33 volunteers in the control group reported catching a cold during the 12 weeks.

Based on these results, which of the following statements is or are supported by the data?

I. Among the volunteers in this trial, those who consumed the vitamin shake were less likely to catch a cold than those who did not.
II. For all adults, consuming the vitamin shake reduces the chance of catching a cold.
III. If the same trial were repeated with another random sample of 300 adults, exactly 18 people in the treatment group would catch a cold.

For a study asking which claims the data support, first compare the outcomes, then check who entered the study, and finally watch for claims about exact future results. Equal-sized groups let you compare counts without calculating percentages. The key distinction is that random assignment chooses treatments, while random sampling chooses participants; confusing them can stretch a result about volunteers to all adults.

Hints

Hint 1
A proportion is the share of a group with a certain outcome. With equal-sized groups, the group with fewer colds also has the smaller proportion. Which group had fewer colds?
Hint 2
Random assignment decides which participants get the shake; random sampling decides who gets picked for the study. Which one would help a result represent all adults?
Hint 3
Random variation means outcomes can change when a trial is repeated. Does a count observed once guarantee exactly the same count among a new group of adults?

Step-by-step

Check the group, the population, and the prediction
Step 1
Compare cold proportions in the trial
No Desmos needed. Equal group sizes make the cold counts enough to compare proportions. A proportion is the share of a group that had a cold. Both groups had $150$ volunteers, so $\frac{18}{150}<\frac{33}{150}$ because $18<33$ . The volunteers who drank the shake had the lower cold proportion, so I is supported.
Step 2
Keep the conclusion within the studied group
The volunteers were randomly assigned: chance chose who drank the shake, not who entered the trial. A random sample would use chance to select participants from all adults. Random assignment helps compare treatments; random sampling decides who the results can represent. Since these participants volunteered, the trial doesn't support II's claim about all adults.
Step 3
Reject an exact prediction for a new trial
A new group could have a different result because of random variation, meaning outcomes can change from one trial to the next. The 18 reported colds are a count from this trial, not a guarantee for another treatment group. So III isn't supported. Among these volunteers, only I is supported. Choice D.

Question 5·Medium·Evaluate Statistical Claims: Observational Studies and Experiments

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this