How to Write a Confidence Interval Conclusion (Step-by-Step)


A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence. It is written as:

Confidence Interval  = [lower bound, upper bound]

We can use the following sentence structure to write a conclusion about a confidence interval:

We are [% level of confidence] confident that [population parameter] is between [lower bound, upper bound].

The following examples show how to write confidence interval conclusions for different statistical tests.

Example 1: Confidence Interval Conclusion for a Mean

Suppose a biologist wants to estimate the mean weight of dolphins in a population. She collects data for a simple random sample of 50 different dolphins and constructs the following 95% confidence interval:

95% confidence interval = [480.5, 502.5]

Here’s how to write a conclusion for this confidence interval:

The biologist is 95% confident that the mean weight of dolphins in this population is between 480.5 pounds and 502.5 pounds.

Example 2: Confidence Interval Conclusion for a Difference in Means

Suppose a zoologist wants to estimate the difference in mean weights between two different species of turtles. He collects data for a simple random sample of 25 of each species and constructs the following 90% confidence interval:

90% confidence interval = [3.44, 12.33]

Here’s how to write a conclusion for this confidence interval:

The zoologist is 90% confident that the difference in mean weight between these two species of turtles is between 3.44 pounds and 12.33 pounds.

Example 3: Confidence Interval Conclusion for a Proportion

Suppose a politician wants to estimate the proportion of citizens in his city who support a certain law. He sends out a survey to 200 citizens and constructs the following 99% confidence interval for the proportion of citizens who support the law:

99% confidence interval = [0.25, 0.35]

Here’s how to write a conclusion for this confidence interval:

The politician is 99% confident that the proportion of citizens in the entire city who support a certain law is between 0.25 and 0.35.

Example 4: Confidence Interval Conclusion for a Difference in Proportions

Suppose a researcher wants to estimate the difference in the proportion of citizens between city A and city B who support a certain law. He sends out a survey to 500 citizens in each city and constructs the following 95% confidence interval for the difference in proportions of citizens who support the law:

95% confidence interval = [0.02, 0.08]

Here’s how to write a conclusion for this confidence interval:

The researcher is 95% confident that the difference in the proportion of citizens who support a certain law between city A and city B is between 0.02 and 0.08.

Additional Resources

The following tutorials provide simple introductions to the most commonly used confidence intervals:

Confidence Interval for a Mean
Confidence Interval for the Difference Between Means
Confidence Interval for a Proportion
Confidence Interval for the Difference in Proportions

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