6.4.7—Mean confidence intervals

A mean confidence interval is estimate ± critical value×standard error, using a normal or t model as specified. The confidence level describes repeated-method coverage.

Use the correct critical distribution, sample size and known/estimated standard deviation; interpret the result in context of the population mean.

A sample mean 42 with margin 3 gives (39,45) at the stated confidence level.

The fixed population mean is not random after the sample is taken; “95% confidence” is not a 95% probability that this interval contains it.