A is a range of values that is likely to contain some population parameter with a certain level of confidence.

When reporting confidence intervals, we always use the following format:

95% CI [LL, UL]

 

where

 

• LL: Lower limit of confidence interval
• UL: Upper limit of confidence interval

The following examples show how to report confidence intervals for different statistical tests in practice.

Example 1: Confidence Interval for a Mean

Suppose a biologist wants to know the mean weight of a certain species of turtles.

She measures the weight of a random sample of 25 turtles and finds the sample mean weight to be 300 pounds with a 95% confidence interval of [292.75 pounds, 307.25 pounds].

Here’s how she might report the results:

A formal study has revealed that the average weight of turtles in this population is 300 pounds, 95% CI [292.75, 307.25].

Example 2: Confidence Interval for the Difference in Means

Suppose a biologist wants to estimate the difference in mean weight between two different populations of turtles.

She collects data for both populations of turtles and finds the mean difference to be 10 pounds with a 90% confidence interval of [-3.07 pounds, 23.07 pounds].

Here’s how she might report the results:

A formal study has revealed that the difference in average weights between the two populations of turtles is 10 pounds, 90% CI [-3.07, 23.07].

Example 3: Confidence Interval for a Proportion

Suppose a biologist wants to estimate the proportion of a certain species of turtles that have spots on their backs.

She collects data for a random sample of turtles and finds that 18% (.18) of them have spots with a 99% confidence interval of [0.15, 0.21].

A formal study has revealed that 18% of turtles in this population have spots on their back, 99% CI [0.15, 0.21].

Example 4: Confidence Interval for the Difference in Proportions

Suppose a biologist wants to estimate the difference in proportions of two species of turtles that have spots on their backs.

She collects data for both populations and finds that the mean difference in the proportions is 7% (.07) with a 95% confidence interval of [0.02, 0.12].

Here’s how she might report the results:

A formal study has revealed that the difference in proportion of turtles who have spots on their backs between the two populations is 7%, 95% CI [0.02, 0.12].

The following tutorials explain how to calculate different confidence intervals in practice: