Skip to Main Content
Main site homepage

QM Course Guide

Confidence Intervals

Confidence Intervals and the Margin of Error

When we take a sample from a population, we use descriptive statistics to summarize that sample data.

However, we can also use sample data to draw conclusions about the population.

Confidence intervals are one way we make inferences about the population.

What is a Confidence Interval?

The CI is an estimate of the range of values within which the population mean is most likely to fall.

Why do we use confidence intervals?

Sample data is collected and used when it is difficult to survey an entire population. We use reliable sample (link sample to populations and sample section 1.a.ii) data to estimate population parameters.

When we hear the term margin of error in news reports, often they are referring to confidence intervals.

How do we calculate the margin of error and CI?

How do we calculate the margin of error and CI?

We use sample data to calculate a margin of error, then add and subtract the margin of error from the sample mean to calculate the CI.

Calculating the margin of error (95% confidence level)



Margin of error =      E    =       1.96s


s = sample standard deviation

n = sample size


Confidence Level

Value of Z





Interpreting the confidence interval

Interpreting the confidence interval

Applying the central limit theorem (link to section on central limit theorem) we know that:

  • with repeated sampling, n > 30
  • using z = 1.96
  • there is a 95% chance that a random confidence interval will cover the true population mean.

What does this really mean?            

We can use the sample data to estimate, with a certain amount of certainty, between which values the population mean lies.