4.2.A—Describe t-distributions

Describe t-distributions.

• t-distributions, also called Student’s t-distributions, form a family of symmetric, bell-shaped, standardized distributions with wider tails than that of the standard normal distribution. Specific t-distributions are identified using a parameter known as the number of degrees of freedom (df), which is based on the sample size(s). When the degrees of freedom are small, the t-distribution has a much narrower peak and fatter tails than a normal distribution. As the degrees of freedom increase, the t-distribution more closely resembles the standard normal distribution (mean μ = 0 and standard deviation σ =1).
• t-distributions are used for finding critical values and test statistics for inferences about a population mean, µ, when the population standard deviation, σ, is unknown and the sample standard deviation, s, must be used instead.