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### Course: Statistics and probability > Unit 11

Lesson 1: Introduction to confidence intervals# Interpreting confidence levels and confidence intervals

When we create a confidence interval, it's important to be able to interpret the meaning of the confidence level we used and the interval that was obtained.

The confidence

*level*refers to the long-term success rate of the method, that is, how often this type of interval will capture the parameter of interest.A specific confidence

*interval*gives a range of plausible values for the parameter of interest.Let's look at a few examples that demonstrate how to interpret confidence levels and confidence intervals.

## Example 1: Interpreting a confidence level

A political pollster plans to ask a random sample of $500$ voters whether or not they support the incumbent candidate. The pollster will take the results of the sample and construct a $90\mathrm{\%}$ confidence interval for the true proportion of all voters who support the candidate.

## Example 2: Interpreting a confidence interval

A baseball coach was curious about the true mean speed of fastball pitches in his league. The coach recorded the speed in kilometers per hour of each fastball in a random sample of $100$ pitches and constructed a $95\mathrm{\%}$ confidence interval for the mean speed. The resulting interval was $(110,120)$ .

## Example 3: Effect of changing confidence level

Suppose that the coach from the previous example decides they want to be more confident. The coach uses the same sample data as before, but recalculates the confidence interval using a $99\mathrm{\%}$ confidence level.

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