STAT303: Secs 102 and 103Summer I 2000Exam #3Form AInstructor: Julie Hagen Carroll1. Don’t EVEN open this until you are told to do so.2. Be sure to mark your section number and your test form (A, B, C or D) on the scantron!3. Sign your name where indicated on your scantron and write your section number, seat number andcomputer number beside it. You will get your scantrons back tomorrow in class. You may keep thisexam.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 20% of your final grade.8. Good luck!1STAT303: 102 and 103 Exam #3, Form A Summer 20001. Oprah wants to increase revenue. She has a lotof female targeted advertising, so her only outletis to increase the advertising targeted at males.You need at least a 20% viewing audience to at-tract advertisers, so she needs to find out if heraudience is at least 20% male. What hypothesesshould she test? Let F indicate females and Mmales.A. H0: µF= µMvs. HA: µF6= µMB. H0: πF= πMvs. HA: πF> πMC. H0: µF= µMvs. HA: µF> µMD. H0: πM= 0.20 vs. HA: πM< 0.20*E. H0: πM= 0.20 vs. HA: πM> 0.20First, this problem is about theproportion of males. So the hypothesesshould involve πM. Furthermore,Oprah needs to find out if heraudience is at least 20% male so theresearch(alternative) hypothesis(HA)should be HA: πM> 0.202. Same scenario: Advertisers are tight with theirmoney, so they want strong proof that there isat least a 20% viewing audience. What α-levelwould the advertising company want Oprahto use?A. α = 0.05 =5% because neither Type I norType II error is critical.B. α = 0.10 =10% because Type I is morecritical.*C. α = 0.01 =1% because Type I is more crit-ical.D. α = 0.10 =10% because Type II is morecritical.E. α = 0.01 =1% because Type II is more crit-ical.Strong proof means a very smallp-value. A Type I error is when wereject H0when H0is true. For thiscase, we would say that more than 20%of the viewing audience is male when itis indeed ≤ 20%. The advertisers wouldthen spend money for no gain. A TypeII error would be that the advertisersdidn’t spend the money (since it was afail to reject) even though they wouldhave gotten a large male audience (H0false).3. Which of the following is true?A. A p-value is how often we would get dataas contradictory as we got even though H0is true.B. A p-value is a measure of the strength ofthe evidence against the null hypothesis.C. A p-value can be used to perform a test ofhypotheses at any significance level.*D. All of the above are true.E. Exactly two of the above are true.A p-value is the probability, assumingthat H0is true, of obtaining a valueof the test statistic at least asextreme(contradictory) to H0as thevalue calculated from the data. It isevidence against H0in favor of theHA.4. Which of the following is NOT a property of thet distribution?A. It is always centered at zero.The t curve, like the z curve, has amean=0.B. It is always wider than the z distribution.Only if we had an infinite sample(infinite degrees of freedom) wouldthe t look exactly like the z.C. It is always symmetric. Again, like thenormal, the t is symmetric (actuallyit’s also bell-shaped only withlonger tails.D. It’s height, at center, increases as the de-grees of freedom increase.The values of t curve varywith the different degrees offreedom. It is always less thanthat of standard z curve at 0.Furthermore, remember that t curvegets closer to z curve as thedegrees of freedom increase.*E. All of the above are properties of thet. See the table of t distribution, tcurve, and z curve.2STAT303: 102 and 103 Exam #3, Form A Summer 20005. What is the correct conclusion that can be madefrom the output above which is testing H0: µ =10 vs. HA: µ > 10?*A. Reject the null at the 10, 5 and 1% levelsand conclude that the true mean is greaterthan 10.B. Reject the null at the 10, 5 and 1% levelsand conclude that the true mean is 10.C. Reject the null at the 10, 5 and 1% levelsand conclude that the true mean is NOT10.D. Reject the null at the 10% level ONLY andconclude that the true mean is greater than10.E. Reject the null at the 10% level ONLY andconclude that the true mean is NOT 10.Because the p-value is 0.003 which isless than 10%, 5%, and 1%, we rejectH0in favor of HAat each level ofsignificance. Hence, we reject H0atthe 10, 5 and 1% levels and concludethat the true mean is greater than 10.6. In the test above, the sample mean, x = 12.6.What would change if we had gotten x = 11instead?A. The conclusion would be the same, sincethe hypotheses are the same.The conclusion depends on the valueof x, s and n we get from the data.The fact that the hypothese are thesame does not affect whether or notthe conclusion will change.*B. The p-value would be larger since the newsample mean is closer to the hypothesizedmean, µ = 10.Because the new sample mean iscloser to the hypothesized mean,the z value will be closer to 0.Therefore, the p-value would belarger.C. The p-value would be smaller since the newsample mean is closer to the hypothesizedmean, µ = 10.D. The sign of the alternative, HA, wouldchange from > to <.We are working with the samehypotheses.E. It’s impossible to tell without rerunning thetest.7. What do we mean by the term confidence in ref-erence to confidence intervals?A. We are confident that our data is random.*B. We are confident that our method producesintervals that contain the parameter (1 −α)100% of the time.C. We are confident that our method pro-duces intervals that contain the parameterα ∗ 100% of the time.We usually consider the α to be theerror rate.D. We are confident that our interval containsthe parameter.The confidence level(ex.95%) refersto the method used to constructthe interval rather than to anyparticular interval.E. We are confident that our method pro-duces intervals that contain the statistic(1 − α)100% of the time.For example, the 95% confidenceinterval for µ means that, if we takesample after sample from the populationand use each one separately to computea 95% confidence interval using thesame method, in the long run roughly95% of these intervals will caputure µ,the population
View Full Document
Unlocking...