Step by step
The question
Question: A poll finds that 58% of voters like the plan, with a margin of error of 4%.
Can we be sure that more than half of all voters like the plan?
1 What the margin means
58% comes from a sample: only some of the people.
The true value for everyone can be a bit different.
The margin of error, 4%, says how far it can be.
± means plus or minus: we go 4% down and 4% up.
The true value is likely in between.
2 Lowest and highest
The lowest likely value: 58% minus 4% is 54%.
The highest: 58% plus 4% is 62%.
3 Draw it
A number line from 48 to 64: a bit of room on each side.
The likely values go from 54% to 62%.
We colour them green.
58%, the sample's answer, is right in the middle.
Half is 50%.
We mark it in red.
4 Inside or outside
Even the lowest likely value, 54%, is more than half.
Careful!
Every likely value is above half.
Very likely, but still not 100% sure.
So yes: it is very likely more than half.
5 Check
Let's check another way: how far is 50% from 58%?
58% minus 50% is 8%.
That is more than the margin, 4%.
Half is not plausible.
So it is right!
Let's look back.
First: what the margin means.
Then: lowest and highest.
Then: draw it.
Then: inside or outside.
Last: check.