Chapter 9: Introduction to Hypothesis Testing

More documents

Recommendations

Info

376 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING W HY Y OU N EED T O K NOW As a business decision maker, you will encounter many applications that will require you to estimate a population parameter. Chapter 8 introduced statistical estimation and included many examples. Estimating a population parameter based on a sample statistic is a component of business statistics called statistical inference. An important component of statistical inference is hypothesis testing. In hypothesis testing, we begin with some belief regarding what the value of a population parameter is, or should be. We then use sample data to either refute or support the initial belief. For example, suppose the Coca-Cola plant in Tampa, Florida, produces approximately 400,000 cans of Coke products daily. Each can is supposed to contain 12 fluid ounces. However, like all processes, the automated filling machine is subject to variation and each can will contain either slightly more or less than the 12-ounce target. The important thing is that the mean fill is 12 fluid ounces. Every two hours, the plant quality manager selects a random sample of cans and computes the sample mean. His initial belief is that the filling process is providing an average fill of 12 ounces. This is his hypothesis. If the sample mean is “close” to 12 ounces, then the sample data would tend to support the hypothesis and the machine would be allowed to continue filling cans. However, if the sample mean is “significantly” higher or lower than 12 ounces, the data would refute the hypothesis and the machine would be stopped and adjusted. Hypothesis testing is performed regularly in many industries. Companies in the pharmaceutical industry must perform many hypothesis tests on new drug products before they are deemed to be safe and effective by the federal Food and Drug Administration (FDA). In these instances, the drug is hypothesized to be both unsafe and ineffective. Then, if the sample results from the studies performed provide “significant” evidence to the contrary, the FDA will allow the company to market the drug. Hypothesis testing is the basis of the legal system in which judges and juries hear evidence in court cases. In a criminal case, the hypothesis in the American legal system is that the defendant is innocent. Based upon the totality of the evidence presented in the trial, if the jury concludes that “beyond a reasonable doubt” the defendant committed the crime, the hypothesis of innocence will be rejected and the defendant will be found guilty. If the evidence is not strong enough, the defendant will be judged not guilty. Hypothesis testing is a major part of business statistics. Chapter 9 introduces the fundamentals involved in conducting hypothesis tests. Many of the remaining chapters in this text will introduce additional hypothesis-testing techniques, so you need to gain a solid understanding of concepts presented in this chapter. Null Hypothesis The statement about the population parameter that will be tested. The null hypothesis will be rejected only if the sample data provide substantial contradictory evidence. Alternative Hypothesis The hypothesis that includes all population values not included in the null hypothesis. The alternative hypothesis is deemed to be true if the null hypothesis is rejected. 9.1 Hypothesis Tests for Means By now you know that information contained in a sample is subject to sampling error. The sample mean will almost certainly not equal the population mean. Therefore, in situations in which you need to test a claim about a population mean by using the sample mean, you can’t simply compare the sample mean to the claim and reject the claim if x and the claim are different. Instead, you need a testing procedure that incorporates the potential for sampling error. Statistical hypothesis testing provides managers with a structured analytical method for making decisions of this type. It lets them make decisions in such a way that the probability of decision errors can be controlled, or at least measured. Even though statistical hypothesis testing does not eliminate the uncertainty in the managerial environment, the techniques involved often allow managers to identify and control the level of uncertainty. The techniques presented in this chapter assume the data are selected using an appropriate statistical sampling process and that the data are interval or ratio level. In short, we assume we are working with good data. Formulating the Hypotheses Null and Alternative Hypotheses In hypothesis testing, two hypotheses are formulated. One is the null hypothesis. The null hypothesis is represented by H 0 and contains an equality sign, such as “,” “,” or “.” The second hypothesis is the alternative hypothesis (represented by H A ). Based on the sample data, we either reject H 0 or we do not reject H 0 . Correctly specifying the null and alternative hypotheses is important. If done incorrectly, the results obtained from the hypothesis test may be misleading. Unfortunately, how you
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 377 should formulate the null and alternative hypotheses is not always obvious. As you gain experience with hypothesis-testing applications, the process becomes easier. To help you get started, we have developed some guidelines for specifying the null and alternative hypotheses. The major point to remember is the “benefit of the doubt” goes to the null hypothesis. Only significant differences will lead to rejecting the null hypothesis. Testing the Status Quo In many cases, you will be interested in whether a situation has changed. We refer to this as testing the status quo, and this is a common application of hypothesis testing. For example, the Kellogg Company makes many food products, including a variety of breakfast cereals. At the company’s Battle Creek, Michigan, plant, Frosted Mini-Wheats are produced and packaged for distribution around the world. If the packaging process is working properly, the mean fill per box is 16 ounces. Every hour quality analysts at the plant select a random sample of filled boxes and measure their contents. They use the sample data to test the following null and alternative hypotheses: H 0 : 16 ounces (status quo) H A : 16 ounces The null hypothesis is reasonable because the line supervisor would assume the process is operating correctly before starting production. As long as the sample mean is “reasonably” close to 16 ounces, the analysts will assume the filling process is working properly. Only when the sample mean is seen to be too large or too small will the analysts reject the null hypothesis (the status quo) and take action to identify and fix the problem. As another example, the Transportation Security Administration (TSA), which is responsible for screening passengers at U.S. airports, publishes on its Web site the average waiting times for customers to pass through security. For example, on Mondays between 9:00 and 10:00 A.M., the average waiting time at Atlanta’s Hartsfield International Airport is supposed to be 15 minutes or less. Periodically, TSA staff will select a random sample of passengers during this time slot and measure their actual wait times. These sample data will be used to test the following null and alternative hypotheses: H 0 : 15 minutes (status quo) H A : 15 minutes Only if the sample mean wait time is “substantially” greater than 15 minutes will TSA employees reject the null hypothesis and conclude there is a problem with staffing levels. Otherwise, they will assume that the 15-minute standard (the status quo) is being met and no action will be taken. Research Hypothesis The hypothesis the decision maker attempts to demonstrate to be true. Because this is the hypothesis deemed to be the most important to the decision maker, it will be declared true only if the sample data strongly indicates that it is true. Testing a Research Hypothesis Many business and scientific applications involve research applications. For example, companies such as Intel, Procter & Gamble, Dell Computers, Pfizer, and 3M continually introduce new and improved products. However, before introducing a new product, the companies want to be sure that the new product is superior to the original. In the case of drug companies like Pfizer, the government requires them to show their product is both safe and effective. Because statistical evidence is needed to indicate that the new product is effective, the default position (or null hypothesis) is it is no better than the original (or in the case of a drug, it is unsafe and ineffective.) The burden of proof is placed on the new product and the alternative hypothesis is formulated as the research hypothesis. For example, suppose the Goodyear Tire and Rubber Company has a new tread design that its engineers claim will outlast its competitor’s leading tire. The competitor’s tire has been demonstrated to provide an average of 60,000 miles of use. Thus the research hypothesis for Goodyear is that its tire is superior, meaning that it will last more than 60,000 miles. The research hypothesis becomes the alternative hypothesis: H 0 : 60,000 H A : 60,000 (research hypothesis) The burden of proof is on Goodyear. Only if the sample data show a sample mean that is “substantially” larger than 60,000 miles will the null hypothesis be rejected and Goodyear’s position be affirmed.
Page 1: Chapter NINE Introduction to Hypoth
Page 5 and 6: CHAPTER 9 • INTRODUCTION TO HYPOT
Page 53 and 54:
CHAPTER 9 • INTRODUCTION TO HYPOT
show all

Chapter 9: Introduction to Hypothesis Testing

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?