I was doing an online course, and the course seemed to suggest that the confidence interval says is that if we have a statement such as the following:
We are XX% confidence interval for some sample statistic is between $\pm$ y.
What this means is that if we take a sample from the population, we can be sure that XX% of the time, the true population statistic will be within: sample statistic $\pm$ y.
I am not sure why this is the case. I was under the impression that the confidence interval gave us a way to tell whether or not the sample statistic was within a certain interval of the true population mean.
Can someone pleas help me understand this?