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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 â€˜significantâ€™ 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:**

- x
_{1}Â = 310 - s
_{1}= 18.5 - n
_{1}= 15

**Sample 2:**

- x
_{2}Â = 300 - s
_{2}= 16.4 - n
_{2}= 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 =Â [-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:**

- x
_{1}= 91 - s
_{1}= 4.4 - n
_{1}= 20

**Technique B:**

- x
_{2}= 86 - s
_{2}= 3.5 - n
_{2}= 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 =Â [2.4550,Â 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: Whatâ€™s the Difference?

4 Examples of Confidence Intervals in Real Life

How to Report Confidence Intervals