If you were to repeat this simulation many times, you'd notice that the first sample (in blue) doesn't always include the true value of the population mean. As you might expect, it will fail to do so about 5% of the time.
* This does not mean that 95% of future samples will have a mean (aka "average") within the confidence interval based on the first sample.

One random sample is drawn from the population and a confidence interval is calculated using the standard deviation calculated from the sample.
Based on that information, the researcher can say, "A sample of 50 observations set the 0.95 confidence interval on the population mean to be (94.901, 100.766). The sample mean was 97.833. The sample estimate of the population standard deviation was 10.26. The confidence interval was calculated using t(49) = 2.021.
A 95% Confidence Interval means that 95% of samples (in the long run) will yield data which includes the true population central tentency. There is no way to know whether or not a particular sample included the true central tendency value.
Because this card is a simulationnot data obtained by measuring something in the real worldand the simulation parameters are the true mean and true standard deviation of the parent population, the software can keep track of which samples did correctly capture the true mean in the confidence interval.In the simulation pictured at the left, 95 of the 100 samples did include the value of the true mean. Five did not and are identified in red.*


One random sample s drawn from the population and a confidence interval is calculated using the true standard deviation (the population standard deviation).
Based on that information the researcher can say, "A sample of 50 observations set the 95% confidence interval on the population mean to be (97.569, 103.113). The sample mean was 100.341. The sample extimate of the population standard deviation was 8.786. The true standard deviation was 10.0. The confidence interval was calculated using z = 1.959964.
The remaining explanation is the same as in the description given above. In this instance only 94% of the samples "captured the true mean."
