# What is an example of a confidence interval

## Confidence interval

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The confidence interval indicates the range of values in which the true value of a parameter (e.g. the mean value) lies with a certain probability. How high this probability should be is determined using the so-called confidence level. For example, a commonly used confidence level is 95%. For example, the confidence interval for the mean is calculated as follows:

With s = standard deviation and z

Now the 95% confidence interval is to be calculated around the determined proportional value.

With s = standard deviation and z

_{1-α / 2}-Quantile of the standard normal distribution. In this case, α is the so-called**Probability of error**So if you want to calculate a confidence interval with a 95% confidence level, then α equals 0.05.### example

One would like to investigate how many people in Germany use a certain smartphone app. 480 random passers-by on a busy shopping street were asked for this. Of these, 15% said they used the corresponding app.Now the 95% confidence interval is to be calculated around the determined proportional value.

### calculation

### Result

With 95% certainty, the proportion of app users is between 11.81% and 18.19% "I don't trust any statistics that I haven't faked myself."

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