Question

A theory suggests that 45 out of 50 samples would contain the population mean. When running the lab/samples I found 96%. 2 of the confidence intervals did not contain the population mean.

Why? Is this because the population parameter is an unknown constant and the invert constructed from a sample is random.

Answer 1

Yes, it is because the population parameter is an unknown constant and the interval constructed from a sample is random.

The theory suggests 45 out of 50 samples would contain the population mean.

As the sample is random, the number of samples that would contain the population mean is also random.

So it is quite possible that the number of samples that would contain the population mean in a lab samples would comprise 96.2% of the samples, as the number of samples that would contain the population mean is random.