Margin of error — Algebra II, what it means and where it is taught
How far the sample result might sit from the truth.
Taught in Algebra II.
Where it is taught
What uses it later
This idea is needed for:
- Confidence interval — The range formed by the estimate plus and minus the margin of error.
Practise this idea
8 questions in the course bank use Margin of error, in Sampling, Simulation & Inference.
Problem 1
A poll is taken only outside a gym. What is the problem?
- The sample is biased
- The sample is too large
- The margin of error is too small
- Nothing
Worked answer
The sample is biased
Gym-goers are not typical of everyone
The tilt is systematic, not random
Problem 2
A poll reports 48% with a margin of error of 4%. Give the lower end of the interval.
Worked answer
44
48-4=44
Problem 3
Why is a random sample preferred?
- It has no systematic tilt
- It is always larger
- It is cheaper
- It avoids the need for a margin of error
Worked answer
It has no systematic tilt
Random selection gives every member an equal chance
So errors are noise, not bias
Problem 4
Estimate the margin of error for a random sample of 400, as a percent.
Worked answer
5
1√400=120=0.05
Problem 5
Estimate the margin of error for a sample of 2500, as a percent.
Worked answer
2
150=0.02
Problem 6
About what sample size gives a margin of error of 5%?
Worked answer
400
√n = 20
n=400
Problem 7
To halve a margin of error, by what factor must the sample size grow?
Worked answer
4
Halving 1√n needs √n to double
So n must quadruple
Problem 8
A 1936 poll asked two million people and still called the election wrong. Why?
- The sample was biased
- The sample was too small
- The margin of error was miscalculated
- The votes were miscounted
Worked answer
The sample was biased
It surveyed car and telephone owners, who were wealthier than average
Size cannot rescue a biased sample