Sampling and statistical inference

Inference means learning about a population from a sample. A random sample gives every member a known chance of selection, so sample statistics (like the sample mean) estimate population parameters (like the population mean) with quantifiable error. The standard error of the mean is the population standard deviation divided by the square root of the sample size — so quadrupling the sample only halves the error. Worked example: with standard deviation 20 and sample size 100, the standard error is 20/10 = 2, and a 95% confidence interval for the mean is roughly the sample mean plus or minus 1.96 x 2, i.e. plus or minus 3.92.