One-Sided or One-Tailed Hypothesis TestsIn most applications, a two-sided or two-tailed hypothesis testis the most appropriate approach. This approach is based onthe expression of the null and alternative hypotheses asfollows: H0: = 170 vs H1: ≠ 170To test the above hypothesis, we set up the rejection andacceptance regions as shown on the next slide, where we areusing = 0.05.
Accept H0Reject H0 Reject H0 0.025 0.95 0.025 Z
In this example, the rejection regionprobabilities are equally split between the twotails, thus the reason for the label as a two-tailed test.This procedure allows the possibility ofrejecting the null hypothesis, but does notspecifically address, in the sense of statisticalsignificance, the direction of the differencedetected.
The difference between the two has to do with howthe null hypothesis is expressed and the implicationof this expression.The first expression above is the more theoreticallycorrect one and carries with it the clear connotationthat an outcome in the opposite direction of thealternative hypothesis is not considered possible.This is, in fact, the way the test is actually done.
The process of testing the above hypothesis isidentical to that for the two-tailed test except thatall the rejection region probabilities are in one tail.For a test, with α = 0.05, the acceptance regionwould be, for example, the area from the extremeleft up to the point below which lies 95% of thearea.The rejection region would be the 5% area in theupper tail.
The Experiment• For 40 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.• 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.Old pizza New pizza -10 0 +10
1. Formulate H1and H0 One-Tailed Versus Two-Tailed Tests• The form of the alternative hypothesis can be either a one-tailed or two-tailed, depending on what you are 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.• A two-tailed test is one where results in either of two directions can lead to rejection of the null hypothesis.
1. Formulate H1and H0 One-Tailed Versus Two-Tailed Tests -- continued• Once the hypotheses are set up, it is easy to detect whether the test is one-tailed or two-tailed.• 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.
1. Formulate H1and H0• As the manager you would like to observe a difference between both pizzas• If the new baking method is cheaper, you would like the preference to be for it. – Null Hypothesis –H0 =0 (there is no difference between the old style and the new style pizzas) (The difference between the mean of the sample and the mean of the population is zero) – Alternative H1 0 or H1 >0 Two tail One tail test test = mu=population mean