Permalink Submitted by Anonymous on April 19, 2016

The sampling distribution, i.e. the distribution of the means of the individual samples is NOT the normal distribution, as this blog states. The sampling distribution is the so-called Student t distribution, which, although similar in shape to the normal (Gaussian) (bell-shaped) has different parameters. In particular, normal distribution does not depend on the sample size while the Student t distribution does (sample size / degrees of freedom is a parameter of Student t). The spread of normal is characterized by variance (standard deviation squared) while the spread of Student t is characterized by the standard error squared.

## Central limit theorem

The sampling distribution, i.e. the distribution of the means of the individual samples is NOT the normal distribution, as this blog states. The sampling distribution is the so-called Student t distribution, which, although similar in shape to the normal (Gaussian) (bell-shaped) has different parameters. In particular, normal distribution does not depend on the sample size while the Student t distribution does (sample size / degrees of freedom is a parameter of Student t). The spread of normal is characterized by variance (standard deviation squared) while the spread of Student t is characterized by the standard error squared.