Question 28·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A sleep researcher selected 150 teenagers at random from a list of teenagers who reported drinking at least one energy drink each day. The 150 teenagers were asked whether they experienced difficulty falling asleep at least three nights per week. Of those surveyed, 80% answered yes.
Which of the following inferences can appropriately be drawn from this study result?
For inference questions like this, first pinpoint who was randomly selected—that defines the population you can generalize to. Next, decide whether the study is observational or an experiment with random assignment; only experiments with random assignment justify causal language like “causes.” Finally, eliminate any choices that (1) talk about a different group (such as all people, adults, or non-drinkers) or (2) make causal claims when the study only supports an association, and choose the option whose scope and strength of claim match what the data and design support.
Hints
Focus on who was actually surveyed
Look closely at the phrase describing how the 150 teenagers were chosen. From what larger group were they selected?
Think about what random selection allows you to conclude
If you take a random sample from a specific group, to which group can you safely generalize your conclusion?
Check for causation versus association
Did the researcher assign some teenagers to drink energy drinks and others not to, or just observe what they already do? Based on that, can you say that energy drinks cause sleep problems?
Eliminate choices that go beyond the data
Cross out any option that talks about people who were not in the sampled group, or that makes a stronger claim than the data support.
Desmos Guide
Verify the percentage calculation (optional)
In Desmos, type 0.8 * 150 to see how many of the 150 teenagers answered yes. This confirms the count but remember that the main question is about what kind of conclusion we can draw, not about computing this number.
Step-by-step Explanation
Identify the sample and the population it represents
The researcher randomly selected 150 teenagers from a list of teenagers who drink at least one energy drink each day. Because the selection was random from this list, the sample can represent the population of teenagers who drink at least one energy drink per day, not all teenagers and not adults.
Recognize what type of study this is
The researcher did not assign some teens to drink energy drinks and others not to; instead, the teens already drank energy drinks, and the researcher just asked a question. This is an observational study (a survey), not an experiment with random assignment, so we can talk about association or proportion, but we cannot claim that energy drinks cause sleep problems.
Translate the numerical result into a verbal statement
In the sample, 80% of these energy-drink-drinking teenagers reported difficulty falling asleep at least three nights per week. Saying “80%” of a group is roughly the same as saying “most” of that group, so an appropriate inference will describe that most members of the same population (teenagers who drink at least one energy drink each day) have that difficulty.
Match the valid inference to the answer choices
Eliminate any choice that (1) talks about all teenagers or adults instead of teenagers who drink at least one energy drink daily, or (2) claims that energy drinks cause sleep problems. The only remaining choice correctly says that most teenagers who drink at least one energy drink each day experience difficulty falling asleep at least three nights per week.