Why don’t we calculate the average of an entire given population instead of computing confidence interval to estimate the population mean? We compute confidence intervals to estimate the true population mean of either a sample (when population standard deviation is unknown) or an entire population (when population standard deviation is known). But I wonder why, if we are given an entire population, why don't we calculate the average of that population instead of computing confidence interval to estimate the population mean since we already have the entire population? I'm not a Math or Stat major so I apologize if my question does not sound "smart".


We compute confidence intervals to estimate the true population mean of either a sample (when population standard deviation is unknown)

"Population mean" refers to the mean of the population. There's no population mean of the sample, only sample mean.

But I wonder why, if we are given an entire population, why don't we calculate the average of that population instead of computing confidence interval to estimate the population mean since we already have the entire population?

We aren't given the entire population. However, in hypothesis testing we, as the name suggests, test hypotheses. The hypothesis generally has at the very least a family of distribution, (e.g. "The null hypothesis is that the data is normally distributed"), and generally includes one or more parameters for that family. When a null hypothesis is that the data is normally distributed and specifies a mean and a standard deviation, we use the z-test. When it says it's normally distributed and specifies a mean but not a standard deviation, we use the t-test.
When we have a null hypothesis that has a specific standard deviation, that doesn't mean we were given that standard deviation, any more than having a null hypothesis with a specific mean means that we were given that mean. It just means that we are testing the hypothesis that that is the correct standard deviation. So technically speaking, if we reject the null with a z-test, that means that the null hypothesis' mean is incorrect, OR its standard deviation is wrong, OR the data is not normally distributed.
Reasons we would use a z-test include:
-The sample size is large enough that the difference between z and t is neglible.
-We have some process that we think may have been altered in a manner that would change the mean, but we think the chances of the standard deviation changing are significantly lower.
-We're using a simpler test for the pedagogical motivation of making things simpler when first introducing students to hypothesis testing.
