Gus, Stan's two alternatives were correct as stated - they were two one sided tests, not a one sided and a two sided test.
Stan, in practical terms, the conclusion 'fail to reject the null' is simply not true. You do in reality 'accept the null'. The catch is that this is, in the research situation, a tentative acceptance - you recognise that you may be wrong, so you carry forward the idea that the null may be 'true' but - on the sample evifdence - probably is not. On the other hand, this should also be the case when you 'reject the null' - the rejection may be wrong, so the rejection is also tentative. The difference is that the null has this privileged position......... In areas like quality control, of course, it is quite clear that you decide, and act as if, the null is true or is not true. Regards, Alan Gus Gassmann wrote: > > Stan Brown wrote: > > > On a quiz, I set the following problem to my statistics class: > > > > "The manufacturer of a patent medicine claims that it is 90% > > effective(*) in relieving an allergy for a period of 8 hours. In a > > sample of 200 people who had the allergy, the medicine provided > > relief for 170 people. Determine whether the manufacturer's claim > > was legitimate, to the 0.01 significance level." > > > > (The problem was adapted from Spiegel and Stevens, /Schaum's > > Outline: Statistics/, problem 10.6.) > > > > I believe a one-tailed test, not a two-tailed test, is appropriate. > > It would be silly to test for "effectiveness differs from 90%" since > > no one would object if the medicine helps more than 90% of > > patients.) > > > > Framing the alternative hypothesis as "the manufacturer's claim is > > not legitimate" gives > > Ho: p >= .9; Ha: p < .9; p-value = .0092 > > on a one-tailed t-test. Therefore we reject Ho and conclude that the > > drug is less than 90% effective. > > > > But -- and in retrospect I should have seen it coming -- some > > students framed the hypotheses so that the alternative hypothesis > > was "the drug is effective as claimed." They had > > Ho: p <= .9; Ha: p > .9; p-value = .9908. > > I don't understand where they get the .9908 from. Whether you test a > one-or a two-sided alternative, the test statistic is the same. So the > p-value for the two-sided version of the test should be simply twice > the p-value for the one-sided alternative, 0.0184. Hence the paradox > you speak of is an illusion. > > Unfortunately for you, the two versions of the test lead to different > conclusions. If the correct p-value is given, I would give full marks > (perhaps, depending on how much the problem is worth overall, > subtracting 1 out of 10 marks for the nonsensical form of Ha). > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102 Fax: +61 03 9903 2007 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
