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 z1-α / 2-Quantile of the standard normal distribution. In this case, α is the so-called Probability of errorSo 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."