STAT302: Secs 507-509Spring 1998Exam #2Fo r m AInstructor: Julie Hagen Carroll1. Don’t even open this until you are told to do so.2. Be sure to mark your section number (507, 508 or 509) and your test form (A, B, C or D) on thescantron!3. Sign your name where indicated on your scantron and write your Tuesday section number and computernumber beside it. Also, you must place your scantron in the correct section stack (for next Tuesday).4. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the scantron. Multiple marks will be counted wrong.5. You will have 60 minutes to finish this exam.6. 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.7. This exam is worth 100 points, and will constitute 25% of your final grade.8. Good luck!1STAT302: 507-509 Exam #2, Form A Spring 19981. What is the power of the test represented in thegraph above?A. 0.511B. 0.05C. 0.95D. 0.489E. Since H0is true, there is no chance of aType II error.2. Which of the following would change the powerof the test?A. reducing the significance level, αB. reducing the sample size, nC. reducing the chance of a Type II errorD. All of the aboveE. Exactly two of the above (excluding D.)3. What is the purpose of confidence intervals?A. to give us a range of plausible values for thesample statisticB. to give us a range of plausible values for thepopulation parameterC. to give us a range of values to find the prob-ability for since a continuous distributionhas no probability at any one pointD. to test whether a hypothesis is trueE. to test if we know what we’re doing4. Suppose we conducted a two-sided hypothesis forH0: µ1= µ2and found the p − value =0.038.What is the best interpretation of this value?A. There is a 3.8% chance of getting a differ-ence in sample means as large as we got (ormore) and the true means still being equal.B. There is a 3.8% chance of rejecting H0.C. There is a 3.8% chance of not rejecting H0.D. There is a 3.8% chance of making a Type Ierror.E. None of the above are appropriate.5. What is the correct conclusion based on thegraph above?A. Reject H0at the 10% level and concludethat the true proportion is not 0.5.B. Reject H0at the 10% level and concludethat the true proportion is greater than 0.1.C. Reject H0at the 10% level and concludethat the true proportion is greater than 0.7.D. Reject H0at the 10% level and concludethat the true proportion is greater than 0.5.E. Reject H0at the 10% level and concludethat the true proportion is not 0.7.6. Suppose we want to find out whether Aggies’GPR’s improve throughout their college career.Which of the following would be the best methodto test this hypothesis?A. Take two independent random samples, oneof freshmen and one of seniors, and comparetheir average GPR’s.B. Take two independent random samples, oneof freshmen and one of seniors, and calcu-late the proportion that had higher GPR’s.C. Take a random sample of seniors, find thedifference in their GPR’s as freshmen andas seniors, and compare that to zero.D. Take a random sample of seniors, find theiraverage GPR and compare that to zero.E. Take a random sample of seniors, find theiraverage GPR and compare that to their av-erage GPR as freshmen.2STAT302: 507-509 Exam #2, Form A Spring 1998Level Mean Std. Err. [Conf. Interval]------------------------------------------90% 22.7 1.032371 20.9098 24.490295% 22.7 1.032371 20.5311 24.868999% 22.7 1.032371 19.7284 25.67167. What is the correct range of the p − value fortesting H0: µ =24.5vs. HA:µ6=24.5?A. p − value > 0.10B. 0.10 >p−value > 0.05C. 0.05 >p−value > 0.01D. p − value < 0.01E. You need a test statistic value to determinethe p − value8. What would be the result of a making a Type Ierror in the hypothesis test above (H0: µ =24.5vs. HA: µ 6=24.5)?A. You conclude that the true mean is 24.5when it actually is not 24.5.B. You conclude that the true mean is 24.5when it actually is 24.5.C. You conclude that the true mean is not 24.5when it actually is 24.5.D. You conclude that the true mean is not 24.5when it actually is not 24.5.E. You can’t make a Type I error unless youfail to reject H0.9. Again referring to the previous data, what is thebest interpretation of the 90% confidence inter-val?A. 90% of the time the true mean will fall inthis interval.B. If we could generate all possible 90% confi-dence intervals for this population, 90% ofthem would be (20.9098, 24.4902).C. If we could generate all possible 90% con-fidence intervals for this population, 90%of them would have µ between (20.9098,24.4902).D. If we could generate all possible 90% confi-dence intervals for this population, 90% ofthem would contain µ.E. None of the above are correct.10. Which of the following is the best interpretationof α in a test of hypotheses?A. α is the proportion of times you will rejectH0.B. α is the proportion of times you will fail toreject H0.C. α is the proportion of times the hypothe-sized value will fall outside a (1 − α)% con-fidence interval.D. α is the proportion of times the hypothe-sized value will fall inside a (1 − α)% confi-dence interval.E. α is the proportion of times you will makea Type I error.A | 13 5.8 1.004007 4.01057 7.58943B | 13 5.8 1.004007 2.73322 8.86678C | 13 5.8 1.004007 3.61245 7.9875411. Which of the following is correct?A. A is the 90%, B is the 95%, C is the 99%B. B is the 90%, C is the 95%, A is the 99%C. A is the 90%, C is the 95%, B is the 99%D. B is the 90%, A is the 95%, C is the 99%E. C is the 90%, B is the 95%, A is the 99%12. What are the hypotheses being tested in thegraph above?A. H0: µ1− µ2= 1 vs. HA: µ1− µ26=1B. H0: σ21− σ22= 1 vs. HA: σ21− σ226=1C. H0: µ1/µ2= 1 vs. HA: µ1/µ26=1D. H0: σ21= σ22vs. HA: σ216= σ22E. H0: µ1= µ2vs. HA: µ16= µ23STAT302: 507-509 Exam #2, Form A Spring 199813. Which of the following is/are true about the datarepresented above?A. Reject the hypothesis that the data shouldbe paired.B. Conclude at the 1, 5 and 10% levels thatthe mean difference is not 0.C. Conclude at the 10% level only that themean difference is not 0.D. Conclude at the 1, 5 and 10% levels thatthe mean difference is 0.E. Exactly two of the above are true.14. Which of the following is the result of increasingthe sample size, n (and not changing any thingelse)?A. The probability of making a Type II
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