
possible value in the population we would find that the true mean is be-
tween the bounds we have set.
If sample sizes are small (n < 30), then the estimate of the sampling
distribution of the means is not normally distributed, but rather follows
what is called a t distribution. The t distribution is generally flatter and
wider than the normal, meaning that values are concentrated somewhat
less in the center and more in the tails. As samples grow larger the distri-
bution approaches the normal distribution: this is the Central Limit
theorem.
Say we have a sample of 20 observations, that is, with 19 degrees of
freedom, and wish to establish the bounds