STAT303: Secs 508 - 510Spring 2005Exam #3Form AInstructor: Julie Hagen Carroll1. Don’t EVEN open this until you are told to do so.2. Be sure to mark your CORRECT section number and your test form on the scantron!3. Sign your name where indicated on your scantron. You may keep this exam.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. This exam is worth 100 points, and will constitute 20% of your final grade.7. 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.8. Good luck!1STAT303: 508 - 510 Exam #3, Form A Spring 20051. Why would you prefer to run a one-sided testsof hypotheses instead of a two-sided?A. If you only cared about whether you werebetter (bigger or smaller, whichever wouldbe appropriate), then the one-sided testwould give you more power.B. The one-sided test requires less data to geta rejection.C. If you knew that the null hypothesis wastrue, you could still get a rejection with aone-sided test.D. You will always get a rejection with a one-sided test if you rejected with a two-sidedtest.E. More than one of the above are true.2. Which of the following is the best interpretationof the p-value = 0.001 when testing H0: µ = 50vs. HA: µ < 50? Note: ¯x = 48.A. 0.1% of the time we will reject the the nullhypothesis.B. 0.1% of the time we will get a sample mean,¯x = 48 or more, when the true mean, µ =50.C. 0.1% of the time we will get a sample mean,¯x = 50 or more, when the true mean, µ =48.D. 0.1% of the time we will get a sample mean,¯x = 48 or less, when the true mean, µ = 50.E. 0.1% of the time we will get a sample mean,¯x = 50 or less, when the true mean, µ = 48.3. Suppose the sample size used in the problemabove was, n = 25. If we took a different randomsample of size n = 40 and still got ¯x = 48, whatwould be the new p-value after running the sameset of hypotheses?A. 0.001 since it’s the same ¯x, hence the samedistance between ¯x = 48 and µ0= 50.B. 0 because it’s impossible to get the exactsame sample mean, ¯x = 48.C. something less than 0.001 since there wouldbe less standard deviations b etween ¯x = 48and µ0= 50.D. something more than 0.001 since therewould be more standard deviations between¯x = 48 and µ0= 50.E. something less than 0.001 since there wouldbe more standard deviations between ¯x =48 and µ0= 50.4. Suppose we ran a hypothesis test at the 5% sig-nificance level. Which of the following is true?A. If we repeatedly sampled the data and ranthe same test, we would reject about 5% ofthe time.B. If we repeatedly sampled the data and ranthe same test, we would fail to reject about95% of the time.C. If we repeatedly sampled the data and ranthe same test, we would make a Type IIerror about 95% of the time.D. If we repeatedly sampled the data and ranthe same test, we would make a Type I errorabout 5% of the time.E. Exactly two of the above are true.5. Suppose I want to test the statement “the meanage of patients at a hospital is more than 60years”. Which of the following sets of hypothesesshould I use?A. H0: µ = 60 vs. HA: µ 6= 60B. H0: π = 60 vs. HA: π > 60, where π isthe proportion of patients over 60.C. H0: π = 0.5 vs. HA: π > 0.5, where π isthe proportion of patients over 60.D. H0: π = 0.5 vs. HA: π 6= 0.5, where π isthe proportion of patients over 60.E. H0: µ = 60 vs. HA: µ > 606. Suppose we tested H0: π = 0.5 vs. HA: π 6= 0.5and got a p-value = 0.016. If we created 90,95 and 99% confidence intervals using the samesample data, which intervals would contain thehypothesized proportion, π = 0.5?A. all threeB. only the 90%C. only the 99%D. both the 90 and 95%E. both the 95 and 99%2STAT303: 508 - 510 Exam #3, Form A Spring 20057. Which of the following best describes the as-sumptions for the Chi-squared test in a contin-gency table?A. Each sample size must be at least 30.B. The variances must be equal.C. The means must be equal.D. The proportions must be equal.E. Each count must be at least 5.8. If I tested H0: µ1= µ2vs. HA: µ16= µ2,and got a p-value = 0.02, which of the followingwould be true?A. I would conclude the means are different atthe 5 and 10% significance levels, but notat the 1%.B. A greater than test, HA: µ1> µ2, wouldhave a p-value = 0.01 if we used the samedata.C. I must have both sample sizes greater than30 if I don’t know the data is normal.D. All of the above are true.E. Exactly two of the above are true.9. What is the advantage of using a paired t-test(Case 10) over either 2 sample t-tests (Cases 8or 9)?A. You only need half as many observations(smaller sample size).B. You have more power (easier to detect adifference).C. You have more degrees of freedom (less con-servative test).D. All of the above are advantages to thepaired t-test.E. Exactly two of the above are advantages tothe paired t-test.10. If we tested H0: π = 0.5 vs. HA: π 6= 0.5and got a p-value = 0.206, which of the followingwould true?A. We would conclude that the true propor-tion, π is not 0.206.B. Since 0.5 is not less than 0.206, we wouldsay we have insufficient evidence to provethe true proportion is not 0.5.C. Since 0.206 is less than 0.5, we would claimthe true proportion is not 0.5.D. We could have made a Type II error.E. None of the above would be true.Race of Respondent * General HappinessGeneral HappinessVery Pretty Not TooHappy Happy Happy TotalWhite 409 730 117 1256Black 46 116 39 201Other 12 26 9 47Total 467 872 165 1504Value df Sig.Chi-Square 24.797 0.00011. What is the Expected Count for Not Too HappyWhite(s)?A. 117B. (117/165 * 117/1256)/1504C. (165 * 1256)/1504D. (165 * 1256)/117E. (165/1504 * 1256/1504)/11712. What are the degrees of freedom for the χ2testin the previous problem?A. 9B. 4C. 3D. 2E. It’s missing from the table, so we can’t say.13. Which of the following is the correct conclusionfor the χ2test in the previous problem?A. Since the p-value is 0, we would concludethat one’s race has an effect on one’s hap-piness.B. Since the p-value is 0, we would concludethat most people are pretty happy.C. Since the p-value is 0, we would concludethat whites are more likely to be very happythan other races.D. Since the p-value is 0, we would concludethat not too many people admit that theyaren’t happy.E. None of the above are
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