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TAMU STAT 303 - ex3asp08

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STAT303 Sec 508-510Spring 2008Exam #3Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers clearly. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. If you have questions, please write out what you are thinking on the back of the page so that we can discuss it afterI return it to you.5. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on theexam. You mus t work alone.6. When you are finished please make sure you have marked your CORRECT section (Tuesday 12:45 is 508, 2:20 is 509,and 3:55 is 510) and FORM and 20 answers, then turn in JUST your scantron.7. Good luck!1STAT303 sec 508-510 Exam #3, Form A Spring 20081. A new method for measuring phosphorus levels in soilis described in a journal article. A sample of 11 soilspecimens, each with a true phosphorus content of 548mg/kg is analyzed with the new method. Based on thesamples, we want to determine if the mean phospho-rus level reported by the new method is significantlydifferent from the true value of 548. What hypothesesshould we test? Let µnewbe the true mean value ofusing the new method and µoldbe the true mean valueusing the previous method.A. H0: µnew= µoldvs. HA: µnew6= µoldB. H0: πnew= πoldvs. HA: πnew6= πoldC. H0: µ = 548 vs. HA: µ 6= 548D. H0: µ = 548 vs. HA: µ < 548E. H0: µnew= µoldvs. HA: µnew< µold2. Which of the following would be an example of a TypeII error in the test above?A. failing to prove the new method produces a differ-ent mean value when it’s actually a better methodB. claiming that the old method is better when thenew method is actually betterC. failing to prove that the new method reports adifferent value when in fact it does have a differentmean valueD. claiming that the new method reports a differ-ent mean when it actually reports the same meanvalueE. reporting that the means are equal when they re-ally are not3. Using the three confidence intervals below, what is thecorrect range of the p-value when testing H0: µ = 4vs. HA: µ 6= 4?90% (4.01057, 7.58943)95% (3.61245, 7.98754)99% (2.73322, 8.86678)A. p-value > 0.10B. 0.10 > p-value > 0.05C. 0.05 > p-value > 0.01D. p-value< 0.01, because 0 isn’t in any of the inter-valsE. You need a test statistic value to determine thep-value4. Which of the following best describes the p-value in atest of hypotheses?A. The p-value is a test statistic used to determinewhether H0should be rejected or not.B. The p-value is the probability, assuming that H0is true, that any sample data would be at least asextreme as that observed.C. The p-value is the probability calculated from thedata that H0is true.D. The p-value is the probability calculated from thedata that H0is rejected.E. The p-value is the probability calculated from thedata that the hypothesized value would fall in a(1 − α) ∗ 100% confidence interval.5. Suppose I need to know whether the true test score isunder 70, so I want to test H0: µ = 70 vs. HA: µ < 70.If I sample the population 20 times and reject (concludethe true mean is under 70) twice (2 out of 20 times),what does this tell me?A. The true mean really is under 70 since I rejectedtwice.B. The true mean is probably not under 70. The 2out 20 rejections, 10%, is just my sample estimateof α, the chance of making a Type I error.C. The true mean is probably not under 70. The 2out 20 rejections, 10%, is just my sample estimateof β, the chance of making a Type II error.D. The true mean is under 70. The 2 out 20 rejec-tions, 10%, is just my sample estimate of α, thechance of making a Type I error.E. The true mean is under 70. The 2 out 20 rejec-tions, 10%, is just my sample estimate of β, thechance of making a Type II error.6. A manufacturer r eceives parts from two suppliers.A SRS of 400 parts from supplier 1 finds 20 de-fective, and a SRS of 100 parts from supplier 2finds only 10 defective. Rather than running ahypothesis test, we calculated a 90, 95 and 99%confidence for the difference in the true propor-tion of defectives for the two suppliers, π1− π2:(−0.103, 0.003), (−0.113, 0.013), (−0.133, 0.033). Whatconclusion could we make?A. Since 0 is in all three confidence intervals, it isplausible that the true proportion of defectives isthe same for the two suppliers.B. Since 0 is in all three confidence intervals, it isplausible that the true proportion of defectives isdifferent for the two suppliers.C. Since 0.05 isn’t in any of the confidence intervals,we would conclude that the true proportion of de-fectives is different for the two suppliers.D. Since 0.01 is in the 95 and 99% confidence inter-val, it is plausible at the 1% level that the trueproportion of defectives is the same for the twosuppliers.E. Since we don’t have a p-value, we can’t come upwith a conclusion.2STAT303 sec 508-510 Exam #3, Form A Spring 20087. In the previous problem, the sample proportions were20/400 = 0.05 and 10/100 = 0.10 for supplier 1 and 2respectively. If supplier 2 had 20 defectives instead ofonly 10, what would have been the difference?A. It would have been less likely that the two trueproportion of defectives were the same.B. It would have been more likely that the two trueproportion of defectives were the same.C. It would not have made any difference since we’retesting the true proportions and not the sampleproportions.D. We would have to run another test, or calculatenew intervals to tell.E. None of the above are correct.8. Which of the following is always a necessary assumptionin test of hypotheses?A. the data must follow a normal distributionB. the data must be from a random sampleC. the true standard deviation must be knownD. All of the above are always necessary.E. Only two of the above are always necessary.9. Remember our last men’s basketball game? Let’s makethat last foul a hypothesis test. The null would be thatno foul occurred and the alternative would be that afoul did occur. If we reject, then we get to make a freethrow; otherwise we don’t get to try. Being that ourguy really was fouled according to later game footagebut they didn’t call it, what happened?A. a Type I errorB. a Type II errorC. a correct decisionD. who knowsE. It was just a sad state of affairs.10. Researchers wish to determine whether the level ofC reactive protein in the


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