When a law firm represents a group of people in a class action lawsuit and wins

Question

When a law firm represents a group of people in a class action lawsuit and wins that lawsuit, the firm receives a percentage of the group's monetary settlement. That settlement amount is based on the total number of people in the group--the larger the group and the larger the settlement the more money the firm will receive.

A law firm is trying to decide whether to represent car owners in a a class action lawsuit against the manufacturer of a certain make and model for a particular defect.If 5% or less of the cars of this make and model have the defect, the firm will not recover its expenses. Therefore, the firm will handle the lawsuit only if it is convinced that more than 5% of cars of this make and model have the defect. The firm plans to take a random sample of 1,000 people who bought this car and ask them if they experienced this defect in their cars.


a. Define the parameter of interest and state the null and alternative hypotheses that the law firm should test.

b. In the context of this situation, describe Type I and Type II errors and describe the consequences of each of these for the law firm.

Explanation / Answer

The parameter of interest is the p-value for the hypothesis

H0 : Percentage of people who own the car of particular make and model in question, having the particular defect is less than 5%

Ha : Percentage of people who own the car of particular make and model in question, having the particular defect is more than 5%

This p-value can be obtained by finding the Z value, based on the data obtained from the survey of 1000 car owners. Generally, we conduct the test at some significance level, and compare p-value against the confidence level we want to achieve.

Type I error - We incorrectly reject the Null hypothesis. That is, we conclude that more than 5% car owners have the defect, when actually that percentage is less than 5%

Type II error - We fail to reject the false null hypothesis. That is, we accept that less than 5% car owners have the defect, when that is not true.

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