Question 5·Medium·Evaluate Statistical Claims: Observational Studies and Experiments
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 experimental-design questions, first translate the setup into simple comparisons (often proportions or averages) to see what actually happened in the study. Then, carefully match each statement to what the data and design allow you to conclude: results within the sample can be described directly; random assignment supports cause-and-effect only for participants; and you usually cannot claim results hold for “all people” unless the sample was randomly selected from that population. Be especially skeptical of claims about exact numbers in future trials, since random variation makes those impossible to guarantee.
Hints
Compare the two groups within this trial
Compute the fraction (or percent) of people who caught a cold in the treatment group and the control group. Which group had a higher proportion of colds?
Pay attention to the population mentioned
Look closely at the wording: does the statement talk about the volunteers in this specific study, or about all adults in general? That affects whether the data can justify it.
Think about repeating the trial
If you ran a similar randomized trial again, would you expect the exact same number of people in each group to catch a cold, or could the numbers change even if the treatment effect is real?
Use study design to limit conclusions
Remember that volunteers in an experiment let you compare groups and look for effects, but they do not necessarily represent every adult in the world.
Desmos Guide
Compare the proportions numerically
In Desmos, type 18/150 and 33/150 (either as separate expressions or in a table). Compare the two decimal outputs to see which group had a higher proportion of colds; this helps you judge statements that describe what happened in this trial.
Step-by-step Explanation
Organize and compare the results
There are 150 volunteers in each group.
- Treatment group: 18 caught a cold.
- Control group: 33 caught a cold.
Compute the proportions:
So, in this trial, a smaller fraction of the treatment group caught a cold than in the control group.
Evaluate Statement I
Statement 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."
This statement talks only about these 300 volunteers in this trial.
From Step 1, of the treatment group caught a cold compared with of the control group. That matches the idea that, among these volunteers, those who took the shake were less likely to get a cold. So Statement I is supported by the data from the trial.
Evaluate Statement II
Statement II: "For all adults, consuming the vitamin shake reduces the chance of catching a cold."
This is a very broad claim about all adults, not just the volunteers.
- The trial used volunteers, not a random sample of all adults.
- The data show what happened in this study, but they do not prove what will happen for every adult.
Therefore, the results suggest a possible effect but do not justify a sweeping conclusion for all adults. Statement II is not supported strongly enough by this one study.
Evaluate Statement III and choose the answer
Statement 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."
Even if the shake has an effect, repeated trials involve random variation:
- The exact number of people who catch a cold will almost certainly change from trial to trial.
- We can expect similar proportions on average, but not the exact same counts like “exactly 18” every time.
So Statement III is not supported.
Putting this all together:
- Statement I is supported.
- Statements II and III are not supported.
The correct answer choice is D) I only.