# Economic Statistics: Hypothesis Testing

This material is replicated on a number of sites
as part of the
SERC Pedagogic Service Project

#### Summary

Students will read a scenario and are asked to interpret Type I and Type II Errors within the context of the problem.

## Learning Goals

A student should gain a greater understanding of the meaning of Type I and Type II errors in hypothesis testing and recognize that these errors have economic implications.

## Context for Use

This activity can be used in an introductory statistics course following the introduction of hypothesis testing, Type I Error and Type II Error.

## Description and Teaching Materials

Students should read the scenario and then describe the implications of a Type I Error and a Type II error in hypothesis testing.

Assume that the mean skate size in the United States is known to be 8.5. Suppose that a U.S. skate manufacturer wants to sell skates in Canada and that he believes that, on average, foot sizes in Canada are smaller than in the United States. If the Canadian foot size is smaller, the skate manufacturer will have to redesign his manufacturing process and invest in different machinery. Suppose that his hypothesis is tested by selecting a random sample of foot sizes in Canada. Define Type I and Type II errors and discuss the consequences of a Type I Error and a Type II error for the manufacturer.

Assume that the mean skate size in the United States is known to be 8.5. Suppose that a U.S. skate manufacturer wants to sell skates in Canada and that he believes that, on average, foot sizes in Canada are smaller than in the United States. If the Canadian foot size is smaller, the skate manufacturer will have to redesign his manufacturing process and invest in different machinery. Suppose that his hypothesis is tested by selecting a random sample of foot sizes in Canada. Define Type I and Type II errors and discuss the consequences of a Type I Error and a Type II error for the manufacturer.

## Teaching Notes and Tips

This is a short exercise to help students transfer a definition of Type I and Type II error into a situation that would have real economic consequences. By answering the question correctly, the student will reinforce the definitions of possible errors that occur in hypothesis testing and the possible real world effects.

## Assessment

Student receives 1 point for attempting to answer the question; 1 point for giving a correct definition of Type I Error; 1 point for giving a correct definition of Type II Error; 1 point for providing a correct consequence of a Type I error, and one point for providing a correct consequence of a Type II error.