Step by step
The question
Question: 250 adults were chosen at random from a city.
Half of them chose to ride a bike to work.
The bike group felt less stressed.
What can the study say?
There are four choices.
First we solve it, the normal way.
Then we pick.
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 ride a bike to work may be different in other ways too.
Careful!
Doing better does not prove the bike caused it.
Something else may make the difference.
So the bike and the better result go together.
But maybe the bike did not cause it.
4 What the study can say
So the study can say: in the city, the bike and the result go together, but maybe the bike 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!
6 Pick the choice
Our answer is linked in the city, maybe not caused.
That is choice B.
7 Why not the others
A is causes it, for the whole city.
Wrong: the adults chose for themselves: no one was put into a group at random.
C is causes it, for people like these.
Wrong: the adults chose for themselves, and they were picked at random from the city.
D is linked, for people like these.
Wrong: the 250 were picked at random, so the link holds for the whole city.
Let's look back.
First: two questions.
Then: how they were picked.
Then: how the groups were made.
Then: what the study can say.
Then: check.
Then: pick the choice.
Last: why not the others.