A survey says 25% with a margin of error of 5%. Is 20% a plausible… Step by Step

Step by step

The question

Question: A survey says 25% with a margin of error of 5%.

Is 20% a plausible value?

1 What the margin means

25% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 5%, says how far it can be.

25% ± 5%

± means plus or minus: we go 5% down and 5% up.

The true value is likely in between.

± = plus or minus

true value: likely within 5% of 25%

2 Lowest and highest

The lowest likely value: 25% minus 5% is 20%.

lowest = 25% − 5% = 20%

The highest: 25% plus 5% is 30%.

highest = 25% + 5% = 30%

3 Draw it

A number line from 16 to 34: a bit of room on each side.

The likely values go from 20% to 30%.

We colour them green.

25%, the sample's answer, is right in the middle.

Now 20%, the value in the question.

We mark it in red.

4 Inside or outside

20% is right at the end of the green part.

The end still counts: it is inside.

= 20% ≤ 20% ≤ 30%

Careful!

Plausible means likely.

It does not mean the true value is 20% for sure.

Careful: plausible = likely, not sure

So yes: 20% is a plausible value.

= yes, 20% is plausible

5 Check

Let's check another way: how far is 20% from 25%?

25% minus 20% is 5%.

That is within the margin, 5%.

So it is right!

25% − 20% = 5%, 5% ≤ 5%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer