Calculus: Type 2 Error

Objectives

• Students will recognize that increasing the probability of a Type I error decreases the probability of a Type II error and vice versa.
• Students will recognize that the sum of the probability of a Type II error and power is 1.
• Students will recognize that as the effect size—the difference between the null hypothesized value and the truth—increases, the power increases (it is easier to see the effect).
• Students will recognize that increasing the sample size decreases the probability of Type I and Type II errors and increases the power.
• Students will recognize that decreasing the standard deviation decreases the probability of Type I and Type II errors and increases the power.

About the Lesson

This activity allows students to experiment with different alpha levels and alternative hypotheses to investigate the relationship among types of error and power.
This activity will give students the following opportunities:

• Experiment with different sample sizes to investigate their relationship with Type I errors, Type II errors, and power.
• Experiment with different standard deviations to investigate their relationship with Type I errors, Type II errors, and power.