9 Questions on Final Exam with Solutions - Introduction to Statistics | STAT 1040, Exams of Statistics

Download 9 Questions on Final Exam with Solutions - Introduction to Statistics | STAT 1040 and more Exams Statistics in PDF only on Docsity! Name: Stat 1040, Fall 2001 Final Test, Thursday December 13, 9:30—11:20 am Show your work. The test is out of 100 points and you have 110 minutes. 1. A recent study in Europe looked at a large group of women of childbearing age. The re- searchers asked each woman how much alcohol they had consumed over the past 12 months. The researchers found that women who drank moderate amounts of alcohol were somewhat less likely to have infertility than women who did not (November, 2001). The study said it “controlled for age, income and religion”. (a) (3 points) Based on the information above, was this a controlled experiment or an observational study? Explain briefly. mar indirtrtion ria task ~ roles van Bed tr dink | nA dtr {b) (3 points) Why did they “control for” age, income and religion? Hirt tachors ney Le nfrundlnn, fokorra_ (e) (4 points) Is this convincing evidence that infertility would decrease if women with infertility started to drink moderate amounts of alcohol? (Note: we are only asking about infertility. There may be other problems introduced by such behavior, but ignore these for answering this question). pots, ; dandony, dato nA cake utile, (d) (4 points) Suggest a possible confounding factor (other than age, income, or religion) and clearly explain why you think it might be a confounding factor. en le lewn ths mahi prob man, net drink end. or de for 4th 2. A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for a one-cup serving. The results may be summarized as follows: a. Average sodium = 240 mg SD = 131 mg x. Average calories = 149 calories SD = 62 calories r= 0.53 {a) Suppose we were to convert our 65 sodium measurements to grams, by dividing each measurement by 1000. Using this new set of measurements, i. (4 points) What will the average and SD of sodium (in grams) be? ave m 240 = 3 p00 O.a4 5, sp=BL = 9, i loco x ii. (3 points} What will the correlation between calories and sodium be now? r= 053, Ae, Ke Aprmd (b) (5 points) Find the regression estimate for the number of mg of sodium in a oné-cup serving of a cereal that has 200 calories per cup. x. brite 2p, = 95, BL. Aoki ala? sp = 053- Te = MIL Baan indy ergy ~ aloe eye = TAD=L I+ 9s TB, | fr 209 abe : . . redliamnz Th [2 |. (2+ 200 Yeaplonton Sipuahcen: adits 13,12 + 10+ Cborite = 257.12 (c} (4 points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 360 calories per cup. 350 obyrty: 39075 2a su, 62 350 in mere Han 35.4, alert tle orton [45 cobeia hy otony tLe doiliagdatin ; Ha veo yeh Lif walhle raninslyga 3. (8 points) According to the U.S. Census Bureau, 68% of Utah residents are 18 years of age or older. What is the chance that in a simple random sample of 100 Utah residents, less than 50% will be 18 years of age or older? foe: [ex 20 PMH foe of drante > 100 sey, AL tar = 41% bee ay = 6.68 sa: §0-68 -33 dre. SD 21/0s¢-0.32 OAT), (00% ~ 99.98% qT NM / \ 49, 986% > SE = ia! od) = ‘ oun “ 37 9 33 = 0.007% 2 a 7. (10 points) A major manufacturer wants to test a new engine to determine whether it meets new air-pollution standards. The average emission of all engines of this type must be no more than 20 parts per million of carbon (Ty engines are manufactured for testing purposes, and the average and SD for this sample of engines are determined to be 24.1 and 3.0 parts per million, respectively. Assuming that these engines are like a simple random sample from a very large population and that the emissions follow the normal curve, is there evidence that this type of engine fails to meet the pollution standard? Set up a null and alternative hypothesis, perform the test, and clearly state your conclusion. a piae = { o (< 30) normal ()) Mall: Imighion, ohorderh mk (ony, = 20 9pm) Dax j > t-te Atternbive: Enioat mn Herdard a0 mot Cam > 20 pen| @ ot. /O-" ao= 3d SE gm? Yio 316 = Ja = 10 Lo _ SE aye, = io = £0 t- Mie 2 4 df= t= 3 (0 Q sn Able 8% 73.25, 204] hoe Mon 05% P~ nba Liar Hen 05 % A . fp. £059 ‘ 7 ‘all ona D negek mall Agdiel P- valet £0.59), ell bill opohchialy oignef 3 triartion stendark month 8. (5 points) The Salt Lake City metropolitan area has about 1.3 million people; the New York City metropolitan area has about 21.2 million — about 16.3 times as many as Salt Lake. Suppose we wish to take a survey to compare attitudes toward environmental policies in these two areas. We are happy with the accuracy (SE) of a survey of 1,200 Salt Lake residents. To get equivalent accuracy in New York, how many New York residents should we survey? Briefly explain. (4200, 0, abou Zhe ume assume, (SE) ands dagrla en. cvmls aise (to bony so pepaltion 2128 in A koa (0 Mmds homer hin aml vine] 9. (5 points) The average age of all 43 presidents when they entered office is 55.3 years, and the SD is 6.2 years. Explain why it would be inappropriate to use these numbers to conduct a significance test on the hypothesis that the average age of entering presidents is 50 years. ve bans thd Hho overigg bn 55 3ayeara tne. This by fA wotmag for te whee “pepblin d US ptyhnls "05 id te puhrrm wm A Memory Aids Please note that these are provided for your convenience, but it is your responsibility to know how and when to use them. rms error = ¥1—r? x SDy SDy lope = slope =r x Sa intercept = avey — slope x avex / number of draws Dt = 4f—_ 'D s number of draws — 1 * s SDpox = 1 faction of 0's x fraction of 1's EVgom = number of draws x aveyoy SEsum = Vuoumber of draws x SDpox EVaxe = AVE Hox SEsum Eave = — ————__——_ SBave number of draws EVy= % of 1's in the box SEsum SEy, - (sae of ama) * 100% SEgigg= Va? +6? where a is the SE for the first quantity, b is the SE for the second quantity, and the two quantities are independent