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A confidence interval conclusion is a statement that summarizes the results of a confidence interval test. It should include the confidence interval, the test statistic, the p-value, the conclusion (reject or fail to reject the null hypothesis), and any other pertinent information.
A is a range of values that is likely to contain a 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 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:
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.
The following tutorials provide simple introductions to the most commonly used confidence intervals: