How to Interpret a Confidence Interval that Contains Zero

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In statistics, a confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence.

If we calculate a confidence interval for the difference between two population means and find that the confidence interval contains the value zero, this means we think that zero is a reasonable value for the true difference between the two population means.

In other words, if a confidence interval contains zero then we would say there is strong evidence that there is not a ‘significant’ difference between the two population means.

The following examples explain how to interpret confidence intervals with and without the value zero in them.

Example 1: Confidence Interval Contains Zero

Suppose a biologist wants to estimate the difference in mean weight between two different species of turtles. She goes out and gathers a random sample of 15 turtles from each population.

Here is the summary data for each sample:

Sample 1:

• x₁ = 310
• s₁ = 18.5
• n₁ = 15

Sample 2:

• x₂ = 300
• s₂ = 16.4
• n₂ = 15

We can plug these numbers into the Confidence Interval for the Difference in Population Means Calculator to find the following 95% confidence interval for the true difference in mean weights between the two species:

95% Confidence interval =  [-3.0757, 23.0757]

Since this confidence interval contains the value zero, this means we think that zero is a reasonable value for the true difference in mean weights between the two species of turtles.

In other words, at a 95% confidence level, we would say that there is not a significant difference in the mean weight between the two species.

Example 2: Confidence Interval Does Not Contain Zero

Suppose a professor wants to estimate the difference in mean exam score between two different studying techniques. He recruits 20 random students to use technique A and 20 random students to use technique B, then has each student take the same final exam.

Here is the summary of exam scores for each group:

Technique A:

• x₁ = 91
• s₁ = 4.4
• n₁ = 20

Technique B:

• x₂ = 86
• s₂ = 3.5
• n₂ = 20

We can plug these numbers into the Confidence Interval for the Difference in Population Means Calculator to find the following 95% confidence interval for the true difference in mean exam scores:

95% Confidence interval =  [2.4550, 7.5450]

Since this confidence interval does not contain the value zero, this means we think that zero is not a reasonable value for the true difference in mean exam scores between the two two groups.

In other words, at a 95% confidence level, we would say that there is a significant difference in the mean exam score between the two groups.

Additional Resources

The following tutorials offer additional information about confidence intervals.

Confidence Interval vs. Prediction Interval: What’s the Difference?
4 Examples of Confidence Intervals in Real Life
How to Report Confidence Intervals