Common Final Exam with Answers for Introduction to Statistics | STAT 1222, Exams of Statistics

Download Common Final Exam with Answers for Introduction to Statistics | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 Fall 2008 Common Final Exam December 11, 2008 Please print the following information: Name: Instructor: Student ID #: Section/Time: THIS EXAM HAS TWO PARTS PART EL. Consists of 25 multiple choice questions worth a total of 60 points. Read all questions carefully. You may do calculations on the test paper. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer, mark the best answer. PART II. This part consists of 3 questions (40 points in total). You MUST show all work for each question in the space provided to receive full credit for that question. If you write your explanations in another part of the test, please indicate accordingly. FOR DEPARTMENTAL USE ONLY: PART II: Questions | 1 | 2] 3 Maximum | 16 | 12 | 12 Score Part I Part I Total STAT1222 Final Exam December 11, 2008 The amounts (in dollars) that 5 randomly selected shoppers spent at Concord Mill Mall are list below: Adle Posi ies fy rt 100 20 0 36 80 Ks ve The 3” of hoo bie, - 1. The mean, median and the standard deviation of the data ate. HY (a) (40.2, 20, 4.50.) 0, 20,36, Go, Ive 0 “abe eee 4 - > y 78? (b) (47.2, 36, © 1681.33.) Kzweame Fx. YR. (47.2, 36, 41.70.) —— = “ee 1254 < uw eoh 326g ovety (ad) (61.2, 50, 51.20.) MU edin ~ WE ee 36 yoo | S28 ered ade) (36.2, 45, 20.70.) E leck) leek zy 645408 6456-3 = | Ae = (ee = 4l- Fost Use the following to answer questions 2, 3 and 4. A recent survey revealed that the mean weight of adults in the U.S. was 5.92 ft with a standard deviation of 0.98 ft. 2 If nothing is known about the shape of the distribution of the adult heights, what rcentage of adults will be bet: 3.96 ft and 7.88 ft? N . rf, percentag will be between an Ne taing brown; byehey ‘ay) At least 75% @ At most 60% SL Proportion of ebyarebion ao belwe te (c) At least 50% . 5-4U 7 W hM-ww {d) At most 40% 3°46 a 88 Mrenia at b hnof (e) At most 20% Melo le 4 : Bx B57, t 3 If the distribution of the adult heights in the U.S. can be considered as approximately bell-shaped, then approximately what percentage of adults will be between 3.96 ft and ‘a 0% Be I - g lup-ed ‘ Between wA- 26 be Lu+ te \) 95% we have OX. — s+ Oe fpr. a7, (d) 81% (e) 68% 4 The z-score of an adult with A height of 5.50 ft is. (a) 2= 253 (b) 2 = 151 Ee Kom. og TAL (c) 2z=0 ~~ ao tn 4 2g (d) 2=-028 -9¢ © 2 = -0.43 STAT1222 page 5 of 13 December 11, 2008 The following is used for questions 12 and 13. In a poll of 764 U.S. citizens taken from 10/17-10/19 by CNN, 49% stated that they would support Barack Obama. Let p denote the ee of all U.S. citizens who supported | + * : Barack Obama. Clee pF % ee , pe 2449, Ge bps °F) ne By 12. Construct a 95% confidence interval for p. is closest to (a) (0.85 , 0.68) CE pat tig feats) 0.455, 0.524 ‘ ) té4 (c) (248, 500) _ (d) (0.57, 0.82) =*4F# ©0354 (e) (0.40, 58) = (45Gb, F254) 13. If no preliminary estimate is available, find the sample size needed to estimate the population proportion p.with 95% confidence. The estimate must be accurate within 3 of p. “ (a) = 30 ye Pal Se), CICS) (S35 )= 1068 (b) n= 1010 i bs GD rates ho pre Fm neny £1 mde wean, fhe pe oyte s (e) n=1087 0 Merewhery Bound pv do rel beg hax, Cate gen f if u vok at who bh oe STAT1222 page 6 of 13 December 11, 2008 The following is used for questions 14, 15 and 16. The following table gives the lifetimes in hours of two batteries for a calculator. We want to test whether the mean lifetimes are different. Two i vw dp engi 4 omwfle; Battery 1 | Battery 2 Lowa m= | mam Giffoul: M, tle Ae 2, = 125.5 | £2 = 120.7 8, = 12.5 | so = 20.6 Aha _14. Choose the correct null and aitcrnchive hypotheses to test the claim. (a) Ho: us > fe versus Ha: pi < pa (b) Ay: ¥1 > F versus Hy : Zy < Fy (c) Ho: pi S fe versus Ha: py > pe — . ca Ao: jy = pe versus Hy: ja x pfg ! wo — dailed (©) Ho: wa < fe versus Ha: ia > be 15. The value of the standardized test statistic is closest to. (a), 0.52 - -on 7 e (b) 0.75 e [¥-%) (dy- die) _ (128-5 - 120-9) — 0 (c) 1.07 ar at ° Sa [20 (SD) 1,20 wh oy oe fe 5 t @ 2.34 \J WAL 367 a 16. Find the p-value for the test and state your conclusion at a = .05. (a). The p-value is 0.0132. The decision: Reject Hy The p-value is 0.2302. The decision: Fail to reject Ho {c) The p-value is 0.1151. The decision: Reject Ho ¢ ing we - tuked {d) The p-value is 0.1151. The decision: Fail to reject Ho feat {e) The p-value is 0.8849. The decision: Fail to reject Ho f “8944 A me P22 (amen iv fuilof2 ) Dect aien Saad S- 0 Ve) c2eisi)= 92 30y. ee} ect Ho dP Z & 2-08) [88 tq [fanw ise a vot Paject Ho - = Wl STAT1222 page 7 of 13 December 11, 2008 The following is used for questions 17, 18 and 19. ra hefer «(liger) A pharmaceutical company claims that its medicine helps reduce the blood sugar le¥el. Table below shows the blood sugar levels (milligrams per deciliter) of 5 patients beforé and after, %, af L Lo Claims Ay di, taking the medicine. Canales } Tine anu cored Member | 1]213)4)5)] “y*%-4, ro “4+! Before | 110 | 140 | 150 | 125 | 130] Hp Ay Lo Hy! +O Ahy| After | 105 | 130 | 135 | 120 | 110 uy ni $s The difference in the blood pressures (before — after) for this sample of four patients results in d= 11 and sg = 6.52. Assume that the blood sugar are approximately normally distributed. te Le 17. Does the medicine help reduce the blood sugar level? Choose the appropriate hypothe- ses to test the claim. (a) Ho: pa = 0 versus Hy: pa #0 (b) Ho: d <0 versus H,:d>0 : Aly: ug <0 versus Hy: pg > 0 > Kes hte dale dq) Ao: pa > O versus Hy: pa <0. . (e) Ho: pa < 0 versus Hy : jtg > 0. of zit, 8,2 6S 2 18. Calculate the value of the standardized test statistic. (b) hs te Ae Ma > Une + o1T43 (c) 0816 Balfn ~ SUSE (d) 1.689 (ce) —2.368 19. Find the rejection region and state your decision at a = .05. (a) Rejection Region: ¢ < 2.353; Decision: Reject Hy (b) Rejection Region: ¢ < —3.182; Decision: Reject Ho Ee Rejection Region: ¢ > 2.132; Decision: Reject Ho tg? 203 EL (d) Rejection Region: ¢ > 3.182; Decision: Fail to reject Hp Reject H, if Ly ele eh (e) Rejection Region: ¢ < ~2.132; Decision: Fail to reject Ho dfs were &, Dabbhiled © STAT 1222 page 10 of 13 December 11, 2008 The following is used for questions 25. The average hours worked during the year x, and the average hourly tip y, are shown in the table below. Hours | 2157 2174 2062 2111 2134 2185 2210 2105 Tips | 2.905 2.97 2.35 2.511 2.791 3.04 3.222 2.493 The regression equation is 7 = 0.0062x — 10.5038. 25. Predict the average hourly tip if the yearly working hour is « = 2200. {a) The predicted amount of tip is $2.56 7 + (b) The predicted amount of tip is $2.61 (c) The predicted amount of tip is $2.81 (d) The predicted amount of tip is $3.14 is © The average hourly wage cannot be predicted —) S tue wet tdo | vlside poe Essoge fe f End of Multiple Choice Section ** ” brewed STAT1222 page 11 of 13 December 11, 2008 Free Response Questions 1. 5 cars were randomly selected. The weights(in thousand pounds) zx and fuel efficiency(MPG) y were measured. The measurements showed that ye Sir=162, Sx = 48.1, Vy =109, Sy? = 2505, Yay = 316.7. (a). (6 pts.) Calculate the correlation coefficient, r, between the weights and the fuel efficiency of the cars. ve £3167) — (62) (104) = 74 34) ee ——— . \eaeen= gop ysl 525)~ 104" (b). .(5 pts.) Find the regression equation. va = § (316%) ~ Ciger) (10%) a 89684 f(yday —loe2y? br Yrwer UE (2 FF 484\Z-04) "OF A 545+ Soe} Br ERLE B04 ye - FtFG84X + Sse | rv o$ (c). (5 pts.) Find the standard error of estimate s.. : es ce ee Fe = )73 ~ bey -wéexy | sos -[G5*3SS0) L109) = qe He8H) \ wee ~—— \ “Het =< Fo+0%G8 STAT 1222 page 12 of 13 December 11, 2008 2. The following is the fat content in percentage for 10 dried whole eggs. ee eK KO Yt 62 55 34 24 80 68 .76 65 .30 40 (a) (4 pts.) Find the five number summaries, é.¢., (Minimum, First Quartile, Second : ; . . fk Quartile, Third Quartile, Maximum). > eee bal s é. ‘) be sition (BH, 30, BY oH, SS, +62, 8S, 48,-76 -¢0 Mins -2 n * 4, feds, 2 4 gute 2 19S 4962 “555 hla +24, -30, 34, 40, Se wT R32 68 p R184 flap = * &e (+24, +34, +885, +68, -80) (b) (4 pts.) Find the inter-quartile range. ThR= R3-kl = +34 {c) (4 pts.) Draw a stem-and-leaf plot. ey 2[y = #24