STAT303: Secs 508Fall 2006Exam #3Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. Be sure to write CARROLL in the space provided on the scantron and your name beneath. Fill in your UIN, sectionnumber and form letter.3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers clearly on the scantron. Multiple marks will be counted wrong.4. You will have 60 minutes to finish this exam.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 must work alone.6. This exam is worth 100 points, and will constitute at least 15% of your final grade.7. Good luck!1STAT303: 508 Exam #3, Form A Fall 20061. We want to test if there is sufficient evidence to say thatthe percentage of students receiving a passing gradein STAT303 is different for juniors and seniors. Howshould we gather the data?A. Take a sufficiently large random sample of juniorsand seniors, make them take STAT 303, and cal-culate the proportion that passes.B. Take a sufficiently large random sample of juniorsand seniors who took STAT303 last semester andcalculate the proportion that passed.C. Take two sufficiently large random samples, one ofjuniors and one of seniors, make them take STAT303, and calculate the proportions that pass.D. Take two sufficiently large random samples, oneof juniors and one of seniors, who took STAT303last semester and calculate the proportions thatpassed.E. Take two sufficiently large random samples, oneof juniors and one of seniors, who took STAT303within the last ten years, and calculate the pro-portions that passed.2. An SRS of 400 parts from supplier 1 finds 20 defective(so p1= 0.05). A simple random sample of 200 partsfrom supplier 2 finds 20 defective (so p2= 0.10). Letπ1and π2be the true proportions of parts which aredefective. A test of H0: π1= π2versus HA: π16= π2isconducted and the resulting p-value is 0.025. Which ofthe following is the b est interpretation of this p-value?A. 2.5% more of the parts from supplier 1 are defec-tive than from supplier 2.B. 2.5% more of the parts from supplier 2 are defec-tive than from supplier 1.C. 2.5% of the time the true proportions are the sameeven though the sample proportions are different.D. 2.5% of the time the sample proportions will be atleast as different as 0.05 and 0.10 even though thetrue proportions are the same.E. None of the above are the correct interpretation.3. Using the same scenario, which of the following is thebest interpretation of the p ower of the test above?A. Power is the probability that we correctly concludeπ16= π2.B. Power is the probability that we incorrectly con-clude π16= π2.C. Power is the probability that we correctly concludeπ1= π2.D. Power is the probability that we incorrectly con-clude π1= π2.E. The power for this test is 1 − 0.025 = 0.975.90% CI: (0.0176, 0.0580)95% CI: (0.0137, 0.0619)99% CI: (0.0061, 0.0695)4. What is the correct range of the p-value for testingH0: π1= π2vs. HA: π16= π2given the three confi-dence intervals for the difference in the true proportionsabove?A. p-value > 0.10B. 0.10 > p-value > 0.05C. 0.05 > p-value > 0.01D. p-value < 0.01E. There isn’t a hypothesized value, so we can’t usethe confidence intervals to decide the p-value.5. What role do assumptions play in a significance test?They guarantee thatA. the data collected follows the appropriate distri-bution.B. the data collected follows the normal distribution.C. the test statistic follows the appropriate distribu-tion.D. the test statistic follows the normal distribution.E. we get the correct conclusion.6. When deciding whether or not to pick up a television se-ries, network executives often show the pilot episode totest audiences. Suppose ABC wants to know if womenreport a grade of ”Favorable” for the pilot of a certainshow at a higher rate than men. What set of hypothesesshould they test?A. H0: πW= πMvs. HA: πW6= πMB. H0: πW≥ πMvs. HA: πW< πMC. H0: πW≤ πMvs. HA: πW> πMD. H0: µW≤ µMvs. HA: µW> µME. H0: µW≥ µMvs. HA: µW< µM7. A car manufacturing company requires that its cars betested for quality. If the quality is good, the cars are dis-tributed to various distributors. If the quality is poor,the cars are held back. Suppose the engineer in chargeuses a null hypothesis which means the quality is good.Which of the following statements correctly describes aType I and Type II error?A. A Type I error would be distributing poor cars,and a Type I I error would be holding back goodcars.B. A Type I error would be distributing go od cars,and a Type II error would be holding back poorcars.C. A Type I error would be holding back good cars,and a Type II error would be distributing poorcars.D. A Type I error would be holding back poor cars,and a Type II error would be distributing goodcars.E. A Type I error would be retesting the good cars,and a Type II error would be not testing the poorcars.2STAT303: 508 Exam #3, Form A Fall 20068. If you ran a greater than test, i.e., HA: µ > µ0insteadof a less than test, which of following would be true?Assume that everything else is the same: the data, α,etc.A. The < p-value would be 1− the > p-value.B. The < α-level would be 1− the > α-level.C. The < test statistic would be the negative of the> test statistic.D. All of the above would be true.E. Only two of the above would be true.9. Suppose the US Department of Education is interestedin knowing if the proportion of high school seniors plan-ning on attending college is more than 60%. They con-duct a hypothesis test with α = 0.05 and get a p-valueof 0.039. What conclusion should they make?A. They should reject H0, and believe that propor-tion of high school seniors planning to attend col-lege is less than 0.6.B. They should not reject H0, and believe that theproportion of high school seniors planning to at-tend college is 0.60.C. They should reject H0, and believe that the pro-portion of high school seniors planning to attendcollege is different than 0.60.D. They should reject H0, and believe that the pro-portion of high school seniors planning to attendcollege is greater than 0.60.E. They should not reject H0, and believe that theproportion of high school seniors planning to at-tend college is different than 0.60.10. Grades in an extremely difficult chemistry course areknown to follow a distribution that is extremely
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