There are two formulas we use when we are computing the confidence interval. One is used when we know the population variance, and the other when we don’t know the population variance. Most likely, we don’t know the population variance.

When the population variance is known, use the z statistic.

When the population variance in unknown, use the Student’s t statistic. The n-1 are the degrees of freedom.

Below is the t statistic table.

So basically the confidence intervals could be summarized as follows. The true population mean falls in the interval defined by the sample mean plus/minus the margin of error (ME).