Have you ever wondered why criminals are innocent until proved guilty, why people would rather decide to pursue a settlement rather than defend the case in court, or even why obvious criminals are labeled innocent in federal courts? Decision making in the justice system assumes a similar approach as hypothesis testing in statistics (Rogers, par. One). Just like statistical decisions, legal decisions result into two types of errors.
This essay, therefore, uses the information from a case study, “July At The Multiplex: A Day At The Movies”, to draw an understanding of type I and type II errors from a legal point of view. To help achieve this, the essay seeks to provide answers to already designed questions as illustrated below.
When would the consortium make a Type I error? A Type II error?
In the case study provided, Tommy threatens to file a class action lawsuit against theatre owners. Working as a consortium, theatre owners weigh their possibilities in court. With a null hypothesis stating that, more than 10% of theatregoers are unhappy with the 20 minutes commercials show routine, the consortium has to make a decision on whether to proceed to court or seek a settlement with Tommy.
In decision making, type I error is made when the null hypothesis is rejected when it is actually true (Easton and McColl, par. 7). In this case, the consortium would make a type I error when they stick to their assumption that only less than10% of moviegoers is unhappy with the commercials hence move on to defend the case in court when a settlement would be more appropriate.
If the consortium move to court on such a decision, Tommy will most likely have a strong case against them and they will not only lose the case, but also incur costs of defending the lawsuit.
On the other hand, Type II error is made when the null hypothesis is accepted when it is actually wrong based on available facts (Easton and McColl, par. 9).
In this case, the consortium would make a type II error when they reach at a conclusion that more than 10% of moviegoers is unhappy with the commercials and hence make a decision to seek a settlement with Tommy instead of proceeding to defend the lawsuit. By so doing, the consortium surrenders while they would have won the case and end up taking the responsibility of resettlement.
In light of this result, what course of action should the consortium, (movie house owners) adopt? Justify your conclusion by applying a statistical evaluation of the accuracy of your result
Suppose the consortium conducted a survey and collected views from 100 moviegoers. Out of these, six (6%) respondents resented the commercials meaning that the null hypothesis above should be rejected. However, this result may not be true when a much larger or smaller data sample is used.
Driving into a conclusive course of action will requires use of test statistics like the computation of z value. z value guides on decisions on rejecting or accepting the null hypothesis depending on the standard normal distribution (Easton and McColl, par. 10).
Using one tail t test and a decision rule of 5% significance level the critical z value is 1.645. z value is computed by dividing the difference between hypothesized proportion (10%) and sampled proportion (6%) by the sampling error (0.03).
The computed z 1.33, which is greater than critical z value; hence a conclusion can be drawn that the null hypothesis be adopted even if the preliminary computations stated otherwise. The consortium should therefore seek a settlement with Tommy instead of proceeding to defend the case in court.
Easton, Valarie J. and McColl, John H. Hypothesis Test. Statistics Glossary, Vol. 1. Web.
Rogers, Tom. “Amazing Applications of Probability and Statistics”. April 2, 1996. Web.