Statistics: Family of t Curves

Objectives

• Students will understand that a family of t-distributions is determined by the number of degrees of freedom.
• Students will recognize that a t-distribution with a small number of degrees of freedom has more area in the tails than a normal distribution.
• Students will recognize that a t-distribution approaches the standard normal distribution as the number of degrees of freedom increases.

Vocabulary

• degrees of freedom
• empirical rule
• mean
• normal probability distribution
• point of inflection
• standard deviation
• t-distribution

About the Lesson

This lesson involves investigating how a t-distribution compares to a normal distribution.
As a result, students will:

• Compare a t-distribution to the standard normal distribution and note that the area in the tails is larger for the t-distribution with one degree of freedom.
• Answer questions about the probability of an outcome occurring for a t-distribution with one degree of freedom and compare this probability to that of the same outcome when the distribution is normal.
• Change the degrees of freedom and observe how the graph of the t-distribution changes.
• Observe that as the degrees of freedom increase, the graph of the t-distribution approaches the graph of the standard normal distribution.