Step by step
The question
Question: 500 voters were chosen at random from a state.
Half of them were chosen at random to read a short fact sheet.
The fact sheet group knew more.
What can the study say?
1 Two questions
To judge a study, we ask two questions.
How were the voters picked?
And how were the groups made?
2 How they were picked
The story says the voters were chosen at random from the state.
So: yes.
At random means all the voters in the state had the same chance to be picked.
So the group is a fair small copy of the whole state.
So what we find can be used for the whole state: true for all voters in the state.
3 How the groups were made
The voters were chosen at random to read a short fact sheet.
So: yes.
Chance made the groups, not the voters.
So the two groups are alike, except for the fact sheet.
So the difference comes from the fact sheet: the fact sheet causes it.
Careful!
Only for the state they were picked from.
Not for all voters everywhere.
4 What the study can say
So the study can say: for all voters in the state, the fact sheet causes this.
5 Check
Let's check with the story.
The first sentence says: chosen at random from the state.
That matches.
The second sentence says: chosen at random to read a short fact sheet.
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.