Step by step
The question
Question: 320 adults were picked at random from a city.
Half of them chose to drink coffee every morning.
The coffee group worked faster.
What can the study say?
1 Two questions
To judge a study, we ask two questions.
How were the adults picked?
And how were the groups made?
2 How they were picked
The story says the adults were chosen at random from the city.
So: yes.
At random means all the adults in the city had the same chance to be picked.
So the group is a fair small copy of the whole city.
So what we find can be used for the whole city: true for all adults in the city.
3 How the groups were made
The adults chose for themselves.
So: no, not at random.
People who choose to drink coffee every morning may be different in other ways too.
Careful!
Doing better does not prove the coffee caused it.
Something else may make the difference.
So the coffee and the better result go together.
But maybe the coffee did not cause it.
4 What the study can say
So the study can say: in the city, the coffee and the result go together, but maybe the coffee is not the cause.
5 Check
Let's check with the story.
The first sentence says: chosen at random from the city.
That matches.
The second sentence says: they chose.
That matches too.
So the answer is right!
Let's look back.
First: two questions.
Then: how they were picked.
Then: how the groups were made.
Then: what the study can say.
Last: check.