STAT303 Secs 509–511Spring 2003Exam #3Form AInstructor: Julie Hagen Carroll1. 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. Pleasemark your answers clearly on the exam. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade ofzero on the exam. You must work alone.5. This exam is worth 100 points, and will constitute 20% of your final grade.6. Good luck!1STAT303 509–511 Exam #3, Form A Spring 20031. Suppose you tested H0: µ1= µ2vs. Ha: µ16=µ2. Your data consisted of two samples with¯x1= 10 and ¯x2= 12 and the resulting p-valuewas 0.806. Which of the following is the bestinterpretation of the p-value for this test?A. There is an 80.6% chance that the two truemeans are equal.B. There is an 80.6% chance of seeing at leastthis big of a difference in sample meanswhen the true means are equal.C. If we took many samples from these samepopulations, 80.6% of the time we wouldfail to reject H0.D. If we took many samples from these samepopulations, 80.6% of the time we wouldsee at least this big of a difference in truemeans when the sample means are equal.E. If we took many samples from these samepopulations, 80.6% of the time we wouldsee at least this big of a difference in samplemeans when the true means are equal.2. Which of the following best describes a Type IIerror in the χ2test for independence?A. We claim the row and column variables areindependent when they actually have somerelationship.B. We claim the row and column variableshave some relationship when they actuallyare independent.C. We don’t prove that there is a relationshipbetween the row and column variables eventhough one exists.D. We don’t prove that the row and columnvariables are independent even though theyare independent.E. We claim we are financially independent,but mom and dad still pay the bills.3. Many people say that dentists make them ner-vous. One way to determine whether someone isstressed, e.g., from having to go to the dentist,is to measure their blood pressure. So, we wantto know if visiting the dentist causes the meanblood pressure to increase. Which method wouldbe the best to use?A. Take a SRS of people who aren’t nervouswhen they go to the dentist and anotherSRS of people who are nervous and comparethe mean blood pressure for the two groupsusing a 2-sample t-test.B. Take a SRS of people who aren’t nervouswhen they go to the dentist and anotherSRS of people who are nervous and comparethe mean blood pressure for the two groupsusing a pooled t-test since it’s likely that thegroups would have quite similar standarddeviations.C. Take a SRS of people, measure their bloodpressure on a day that they aren’t going tothe dentist and again the day they do go,compare the results using a paired t-test.D. Take a SRS of people who aren’t nervouswhen they go to the dentist and anotherSRS of people who are nervous, measuretheir blood pressure before and after vistingthe dentist and compare the results using aχ2test for proportions since nervous or notis a categorical variable.E. none of the above4. Does cooking in iron pots increase the iron con-tent of food? A study was done using anEthiopian beef dish. Four samples each werecooked in iron, clay and aluminum pots. Whatare the appropriate degrees of freedom for theF -test?A. numerator df = 2, denominator df = 9B. numerator df = 2, denominator df = 11C. numerator df = 3, denominator df = 12D. numerator df = 3, denominator df = 4E. numerator df = 2, denominator df = 32STAT303 509–511 Exam #3, Form A Spring 20035. The composition of the earth’s atmosphere mayhave changed over time. One attempt to discoverthe nature of the atmosphere long ago studiesthe gas trapped in bubbles inside ancient am-ber. The gas in bubbles within amber shouldbe a sample of the atmosphere at the time theamber was formed. Measurements on specimensof amber from the late Cretaceous era give thesepercents of nitrogen:63.4 65.0 64.4 63.3 54.864.5 60.8 49.1 51.0If we also know that the present nitrogen level inour atmosphere is 78.1%. Which set of hypothe-ses should we test to determine if the nitrogenlevel has changed over time?A. H0: πold= πnowvs. HA: πold6= πnowB. H0: πold= 0.781 vs. HA: πold6= 0.781C. H0: µold= µnowvs. HA: µold6= µnowD. H0: µold= 78.1% vs. HA: µold6= 78.1%E. H0: µnow= 78.1% vs. HA: µnow6= 78.1%6. What assumptions are necessary for us to be ableto perform the test in the last problem?A. The sample of amber (actually the nitrogenlevel in the bubbles in the amber) must berandom.B. The nitrogen levels in ancient amber mustfollow a normal distribution or we have touse a non-parametric procedure.C. The sample size must be large enough fornπoldand nπnowto be greater than 10.D. All of the above are necessary.E. Only two of the above are necessary.7. When testing a statistical hypothesis, we fail toreject H0at the α% level ifA. H0is true.B. the hypothesized value under H0is lessthan the sample value.C. α is less than the p-value of the test statis-tic.D. All of the above are true.E. None of the above are true.8. The power of a test isA. the probability that H0is true.B. the probability that H0is false.C. how often we correctly reject H0.D. the probability of rejecting a true H0.E. Exactly two fo the above are correct.9. A study was done to determine whether tak-ing painkillers before surgery (the experimen-tal group) was more effective than the regularpractice of waiting until after to start the paintherapy (the control group). After 912weeks, 12of the 60 men in the experimental group werestill feeling pain, and 18 of the 30 in the controlgroup were still feeling pain. Which test shouldbe used?A. the paired t-test for mean differences, pair-ing the men with similar pain symptoms.B. the pooled t-test for the difference of meanssince it’s likely the the variability of the twogroups is the same.C. the 2-sample t-test since both samples hadmore than 30 men.D. the 2-sample z-test for proportionsE. the 2-sample z-test for means10. When is a confidence interval more ‘useful’ thana hypothesis test? Consider only means here,and not proportions.A. when we want to run a two-sided testB. when we want an idea of the size of effect(mean or difference)C. when we don’t know the true standard de-viationD. when we don’t
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