Education Technology

Family of t Curves

Published on 11/30/2011

Activity Overview

This lesson involves investigating how a t-distribution compares to a normal distribution.

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.