1. Information Technology and Decision Making Information Technology and Decision Making Example 10.1 Experimenting with a New Pizza Style at the Pepperoni Pizza Restaurant Concepts in Hypothesis Testing

2. Information Technology and Decision Making Information Technology and Decision Making 2 Background Information The manager of Pepperoni Pizza Restaurant has recently begun experimenting with a new method of baking its pepperoni pizzas.

3. Information Technology and Decision Making Information Technology and Decision Making 3 Background Information – cont’d He believes that the new method produces a better-tasting pizza, but he would like to base a decision on whether to switch from the old method to the new method on customer reactions. Therefore he performs an experiment.

4. Information Technology and Decision Making Information Technology and Decision Making 4 The Experiment For 100 randomly selected customers who order a pepperoni pizza for home delivery, he includes both an old style and a free new style pizza in the order.

5. Information Technology and Decision Making Information Technology and Decision Making 5 The Experiment – cont’d All he asks is that these customers rate the difference between pizzas on a -10 to +10 scale, where -10 means they strongly favor the old style, +10 means they strongly favor the new style, and 0 means they are indifferent between the two styles. Once he gets the ratings from the customers, how should he proceed?

6. Information Technology and Decision Making Information Technology and Decision Making 6 Hypothesis Testing This example’s goal is to explain hypothesis testing concepts. We are not implying that the manager would, or should, use a hypothesis testing procedure to decide whether to switch methods.

7. Information Technology and Decision Making Information Technology and Decision Making 7 Hypothesis Testing – cont’d First, hypothesis testing does not take costs into account. In this example, if the new method is more costly it would be ignored by hypothesis testing. Second, even if costs of the two pizza-making methods are equivalent, the manager might base his decision on a simple point estimate and possibly a confidence interval.

8. Information Technology and Decision Making Information Technology and Decision Making 8 Null and Alternative Hypotheses Usually, the null hypothesis is labeled H o and the alternative hypothesis is labeled H a. The null and alternative hypotheses divide all possibilities into two nonoverlapping sets, exactly one of which must be true.

9. Information Technology and Decision Making Information Technology and Decision Making 9 Null and Alternative Hypotheses – cont’d Traditionally, hypotheses testing has been phrased as a decision-making problem, where an analyst decides either to accept the null hypothesis or reject it, based on the sample evidence.

10. Information Technology and Decision Making Information Technology and Decision Making 10 One-Tailed Versus Two-Tailed Tests The form of the alternative hypothesis can be either a one-tailed or two-tailed, depending on what the analyst is trying to prove. A one-tailed hypothesis is one where the only sample results which can lead to rejection of the null hypothesis are those in a particular direction, namely, those where the sample mean rating is positive.

11. Information Technology and Decision Making Information Technology and Decision Making 11 One-Tailed Versus Two-Tailed Tests – cont’d A two-tailed test is one where results in either of two directions can lead to rejection of the null hypothesis. Once the hypotheses are set up, it is easy to detect whether the test is one-tailed or two- tailed.

12. Information Technology and Decision Making Information Technology and Decision Making 12 One-Tailed Versus Two-Tailed Tests – cont’d One tailed alternatives are phrased in terms of “>” or “<“ whereas two tailed alternatives are phrased in terms of “  ” The real question is whether to set up hypotheses for a particular problem as one-tailed or two- tailed. There is no statistical answer to this question. It depends entirely on what we are trying to prove.

13. Information Technology and Decision Making Information Technology and Decision Making 13 Types of Errors Whether or not one decides to accept or reject the null hypothesis, it might be the wrong decision. One might reject the null hypothesis when it is true or incorrectly accept the null hypothesis when it is false. These errors are called type I and type II errors.

14. Information Technology and Decision Making Information Technology and Decision Making 14 Types of Errors – cont’d In general we incorrectly reject a null hypothesis that is true. We commit a type II error when we incorrectly accept a null hypothesis that is false. These ideas appear graphically below.

15. Information Technology and Decision Making Information Technology and Decision Making 15 Types of Errors -- continued While these errors seem to be equally serious, actually type I errors have traditionally been regarded as the more serious of the two. Therefore, the hypothesis-testing procedure factors caution in terms of rejecting the null hypothesis.

16. Information Technology and Decision Making Information Technology and Decision Making 16 Significance Level and Rejection Region The real question is how strong the evidence in favor of the alternative hypothesis must be to reject the null hypothesis. The analyst determines the probability of a type I error that he is willing to tolerate. The value is denoted by  and is most commonly equal to 0.05, although sigma=0.01 and sigma=0.10 are also frequently used.

17. Information Technology and Decision Making Information Technology and Decision Making 17 Significance Level and Rejection Region – cont’d The value of  is called the significance level of the test. Then, given the value of sigma, we use statistical theory to determine the rejection region.

18. Information Technology and Decision Making Information Technology and Decision Making 18 Significance Level and Rejection Region – cont’d If the sample falls into this region we reject the null hypothesis; otherwise, we accept it. Sample evidence that falls into the rejection region is called statistically significant at the sigma level.

19. Information Technology and Decision Making Information Technology and Decision Making 19 Significance from p-values This approach is currently more popular than the significance level and rejected region approach. This approach is to avoid the use of the  level and instead simply report “how significant” the sample evidence is.

20. Information Technology and Decision Making Information Technology and Decision Making 20 Significance from p-values – cont’d We do this by means of the p-value.The p- value is the probability of seeing a random sample at least as extreme as the sample observes, given that the null hypothesis is true. Here “extreme” is relative to the null hypothesis.

21. Information Technology and Decision Making Information Technology and Decision Making 21 Significance from p-values – cont’d In general smaller p-values indicate more evidence in support of the alternative hypothesis. If a p-value is sufficiently small, almost any decision maker will conclude that rejecting the null hypothesis is the more “reasonable” decision.

22. Information Technology and Decision Making Information Technology and Decision Making 22 Significance from p-values – cont’d How small is a “small” p-value? This is largely a matter of semantics but if the −p-value is less than 0.01, it provides “convincing” evidence that the alternative hypothesis is true; −p-value is between 0.01 and 0.05, there is “strong” evidence in favor of the alternative hypothesis;

23. Information Technology and Decision Making Information Technology and Decision Making 23 Significance from p-values – cont’d −p-value is between 0.05 and 0.10, it is in a “gray area”; −p-values greater than 0.10 are interpreted as weak or no evidence in support of the alternative.