forget the statement of the null build a CI ... perhaps 99% (which would correspond to your .01 sig. test) ...
let that help to determine if the claim seems reasonable or not in this case ... p hat = .85 .. thus q hat = .15 stan error of a proportion (given SRS was done) is about stan error of p hats = sqrt ((p hat * q hat) / n) = sqrt (.85 * .15 / 200) = about .025 approximate 99% CI would be about p hat +/- 2.58 * .025 = .85 +/- .06 CI would be about .79 to .91 ... so, IF you insist on a hypothesis test ... retain the null personally, i would rather say that the pop. proportion might be between (about) .79 to .91 ... doesn't hold me to .9 problem here is that if you have opted for .05 ... you would have rejected ... (just barely) At 02:39 PM 11/29/01 -0500, you 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. > >Now as I understand things it is not formally legitimate to accept >the null hypothesis: we can only either reject it (and accept Ha) or >fail to reject it (and draw no conclusion). What I would tell my >class is this: the best we can say is that p = .9908 is a very >strong statement that rejecting the null hypothesis would be a Type >I error. But I'm not completely easy in my mind about that, when >simply reversing the hypotheses gives p = .0092 and lets us conclude >that the drug is not 90% effective. > >There seems to be a paradox: The very same data lead either to the >conclusion "the drug is not effective as claimed" or to no >conclusion. I could certainly tell my class: "if it makes sense in >the particular situation, reverse the hypotheses and recompute the >p-value." Am I being over-formal here, or am I being horribly stupid >and missing some reason why it _would_ be legitimate to draw a >conclusion from p=.9908? > >-- >Stan Brown, Oak Road Systems, Cortland County, New York, USA > http://oakroadsystems.com >My reply address is correct as is. The courtesy of providing a correct >reply address is more important to me than time spent deleting spam. > > >================================================================= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >================================================================= _________________________________________________________ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
