Student t-verdeling

Normal distributions are used for populations with known standard deviations. However, for most real-world data, the population standard deviation is unknown.

For such populations, the Student t distribution can estimate the population mean using a sample statistic. In this case, the sample mean is the best point estimate for the population mean.

This distribution can be used for simple random samples from a normally distributed population or when a sample size is greater than 30.

For a normally distributed population, the Student t distribution can be given as shown for all values of size n.

Since the estimated sample size is small, the confidence intervals in this distribution are wider, with larger critical values than the normal distribution. The margin of error can be evaluated using the given formula, which helps compute the confidence interval limits.

The Student t distribution shows sample variability. Although symmetrical, it has a wider distribution and represents greater variability than the normal distribution. It always has a standard deviation greater than 1.

However, as the sample size increases, the Student t distribution comes closer to a normal distribution.