Assumptions: Observations are independent of one another. The data come from a normal distribution with mean, μ, and variance, σ2, (i.e. x i ∽ N(μ,σ2)) with σ2 known or large n with σ2 known. Note: This test will not be stressed as the population variance is almost always unknown in real life. In addition, software such as SPSS does not even offer this option for the latter reason.
The one sample z-test and confidence interval are used when the true population variance, σ2, is known. This is almost never the case, but for large samples we sometimes treat the sample variance as the population variance. In addition, in order to calculate the true population variance you would need to know the true population mean, μ thus making this section more of academic value than practical value.
A (1 - α)100% confidence interval for μ is,
