Introduction to Statistics - Final Exam Solved | STAT 1222, Exams of Statistics

Download Introduction to Statistics - Final Exam Solved | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 Spring 2008 Common Final Exam May 1, 2008 PLEASE PRINT THE FOLLOWING INFORMATION: Name: Instructor: Student ID: Section/Time:_ THIS EXAM HAS TWO PARTS. PARTI. Consists of 25 multiple choice questions (2.4 points each). Read all questions carefully. You may do calculations on the test paper. Mark the number of the opscan sheet corresponding to the test question number with a Number 2 pencil or a mechanical pencil with HB lead. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer; mark the best answer. Please make sure that your name and ID appear on the opscan sheet in the spaces provided. PART Ti. This part consists of 3 problems (a total of 40 points), 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. At the end of the examination, you MUST hand in this test bookiet, your answer sheet and all scratch paper. FOR DEPARTMENTAL USE ONLY: PART IE [ Questions 1 2 i 3 Score | T “Part ] Pat | TOTAL STAT 1222 FINAL EXAM a, Use the following sample data to answer questions 1 and 2. 1. The sample mean and standard deviation, (Z, s) are a) (0,1) b) (1,1) ce) (4,2) dy (1,8) ee) (4,4) 2. The test scores of 15 employees enrolled in a CPR training course are listed below. Find the first, second, and third quartiles (Q1, Q2, Qs) of the test scores. 139 18 15 14 21 20.5 18 37 fa (9 16 Bt Golly 8, i Goi 8.25048 (bye 15 18) rire () @1 17) Medion = is ¥. + (a) (9 16 21) il: 7 £0 eee “co @ 2 (e) (1 : for 8 21 37) AZ 2 1 Use the following information to answer questions 3 and 4. 69/45/99. According to the records of a major hospital, the birth weights of newborns has a gym bw tetead -metric and bell-shaped frequency distribution with a mean-of 6.8 pounds and a standard deviation of 0.) pound. ®— beth weight, Mb, Pies 3. Approximately, what percent of newborn babies weigh under 6.3 pounds? (a) 50% outside omen: teo-ge> 327. (b) 2.5% lail ¢ 32 . ee A (c) 95% bH- ‘ ne ig f. $3 5G 64 bg $3 og Oe “4 i (a) 68% hou W ay - ug Mer te Ow MOE MES BE pase 4. If the z-score corresponding to the weight of a newborn baby is 3, which L Seoves 3 eight? of the following statements best describes the newborn’s weight? Wess Hoe ° I server © This is'a very heavy baby in comparison to other newborn babies. is % Su ev (b) This is a very light baby in comparison to other newborn babies. fe ickt of A ‘ (c) This is an average weight baby. j (d) This is a somewhat below average weight baby. thee WLan (ec) One cannot make any statement since only the z-score corresponding to the weight is given. STAT 1222 FINAL EXAM SPRING 2008 Use the following information to answer questions 12 and 13. ‘The mean room and board expense per year at a four-year college is $6850 with a standard deviation of $1200. You randomly select 36 four-year colleges and consider the sample mean & AA= 685°, Pro , wz>b 12. Which of the following statements regarding the distribution of % is correct ? fi } & is approximately normally distributed with mean p; = 6850. and standard deviation o; = 200 (b) # is approximately normally distributed with mean ji; = 6850 and standard deviation og = 7200 . (c) £ is approximately normally distributed with mean 4; = 200 and standard de- viation og = 6850 : (d) Z is approximately normally distributed with mean Las = = 6850 and standard deviation a; = 1200 (e) None of the above. _ on For 4 7,30 4 & in ev aeal ; Az eM, rz - YA 18, The probability that the sample mean # is less than $7000 isabout ls = gy SO, wos CR F toe) Tzz ILO 20H Oar Pit 2 Fove ~4$50 7} 36 (ec) 0.8106 ———=<—" (d) 0.7506 -7 260 . (ec) 0.1977 "(24 4S) 2 .7F3y | 22° 14, The advertising department of a nationally circulated inagazine wishes to estimate the mean age of its subscribers(to within 0.5 yearywith 90% confidence. If they estimate that the standard deviation of the ages Of their subscribers is 5 years, find the required sample Size fy Sawble Cire fy x: “ Ye (<= )* (a) 1 es ar fo tee 9) = 2 E 49 Ce AOL | tee bus. ye (ess mn S anwple $ ie Youn to ; (e) 13 tel | wbe nes, WA > Foe bors. vt ati STAT. 1222 FINAL EXAM SPRING 2008 15. The length of time employees have worked at a corporation is normally distributed with a mean of 11.2 years and a standard deviation of 2.5 years. In-acompamy-cotback, the lowest 10% in seniority are to be laid off. What is the maximum length of time an employee could have worked and still be laid off? Stebi> Solve for ®- x—> lg tle A dime 10 ~ . TUS a a Me Wye 210 (c)/8 z=7 ° Os Zool. qe Xi } Sle a ce eo SWS (-prgi(~s)- G FP+ucK 16. You randomly select10 mortgage lenders and determine the current mortgage interest rate at each. The sample mean rate is 5.9% with a sample standard deviation of 0.4%. Assuming that the interest rates are approximately normally distributed, a 95% = ¢_ confidence interval for the population mean mortgage interest rate is closest to = Oe Wee, R25 h | we 4 by /561<p<6ig ©-L+% x th ; a f. awe =, (c) 5.76 <p < 6.08 Ol ca + w Lez 29262 () 5.65 <p < 6.15 (5-4 TF 2.262 x(t) 4 +2961 (e) 570.<p< 611 — = > SAT GbE MN & big gy 17 In order to estimate the proportion of all credit card holders who pay all their credit card bills in full each month, a credit counseHi® bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month: A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is closest to C y fear = ug a 7. (a) .282 + .010 we se c 14 ) y. OA ; vobor tion (b) .282 + .027 C. Vite eo R, jez A beh (c) .282 + .042 0 bz 4 anab le Qe 3 “A (2) .282 + 035 b - {2% @ . 9622 propos tion “A Hy { + .055 CT i «2422 FY 2ees Create -_ Ke ? - = jo po t#8, Z,2 7-S4s rs 2 a \ 460 STAT 1222 FINAL EXAM SPRING 2008 18. Given that the p-value for a test of hypothesis is = .0323, then at the significance level a = .05, which of the following statements is the correct decision? (a) Reject Hp because a is less than p. (b) Do not reject Ho because p is less than a. (c) Do not reject Hy because @ is less than p. @& Reject Hy because p is less than a. (e) No decision can be made because not enough information is given. Use the following information to answer questions 18, 20, and 21. A medical researcher claims that less than 20% of all adults in the United States are allergic to a medication. In a random sample of.125 adults in the United States, 18 say they have such an allergy. Claiws P Eek He: bP? Ha: P Zeb 19. State the correct null and alternative hypotheses to check the researcher's claim. (a) Hyp: p< .20 vs. H,: p> .20 (b) Hy : p= 20 vs. Hy: p #20 (c) Hy: p> .20 vs. Hy: p< 20 AY Hy: p> .20 vs. Ha: pe 200-3 bff -failed (e) Hp: P< .20 vs. H,: H> 20 20. The value of the standardized test statistic is about (a) 2=15 bit : 144 | te oda 220 ee o 2 Pe (ones - pete Menkes Jee 12 (d) z= —2.32 aes oes “panes 21. The p— value of the test is about 4099 left- tniled fet ; So PF valun = (a) (b) .9406 gon bflf shsanved 2 an WN pe 084 4406 at, r (e) .0901 1S STAT. 1229 FINAL EXAM FALL 2008 PART I] FREE RESPONSE QUESTIONS 1. Is cardiovascular fitness (as measured by time to exhaustion from running on a tread- mill) related to an athlete’s performance in a 20-km ski race? The following data on x = treadmill time to exhaustion (in minutes) and y = 20-km ski time (in minutes) summarizes the results of a study on this subject. [2 | oy 7.7 | 71.0 8&4 | 714 8.7 | 65.0 9.0 | 68.7 9.6 | 644 9.6 | 69.4 10.0 | 63.0 10.2 | 64.6 10.4 | 66.9 | 11.0 |-62.6 11.7 | 61.7 n=ll Se 1063 STy = 728.70 Soe? = 1040.95 Sry? = 48,390.79 Say = 7009.91 (a) Assuming the existence of a linear relationship, find the equation of the regression lme § = ma + 6 relating y to z. we WORT = (ie (Fes: te), Ne - Le BRS 45) — (106° 3)> ~ Ww Ciuaras) ~( EX = 46636 be 2 GL UY SS — (13438) (46635) 5 * aE _- a 5 66-4459 4°29 hee 245s Wr -2°335S% +88 - FITS (b) Find the coefficient of correlation and interpret its meaning in the contest of the problem. Viz 80009-4193 — ( 106-3) ( 429-40? avi 95) ~ (0bo3™ jee 390-79) ~ FUS+ PD —~ - F4G 1 STAT 1222 FINAL EXAM FALL 2008 c. Find the standard error of the estimate. Be = | yar ta ~ (se TMF) 890) — Cassis) (7044 \ tb- be a d. Predict the 20-km ski time of athletes whose treadmill time to exhaustion is 9.5 minutes. \ Xo= to) we Chute Xp is out of © £ rf toe. a } pb senved x's ) i om Cannel pre 1G Mang Moqveniom line. e. Construct a.95% prediction interval for the 20-km ski time of an athlete whose treadmill time to exhaustion is 9.5 minutes. A Xz 4S Yr — 2+ B¥35(4-5) + B8-FYSS ~ 66 °6LF3 ar. Tar Chi YFE, Bot sy fiety “Cyt VV wEx (8 x) > dfie neared: gt ck, fot 2-262 | er 2E 2 9-66 86 «il * en Fe (1-260) (2-942) hyp ty NAG = 966%) yoo UC 1040-95) - 1063" oe AF GES Lf GPE =< 66 +6173 + S-1?6¢ STAT 1222 FINAL EXAM. FALL 2008 2. Ultrasound is often used in the treatment of soft tissue injuries. In an experiment to investigate the effect of an ultrasound and stretch therapy on knee extension, range of motion was measured both before and after treatment: for a sample of 7 physical therapy patients. A set of data appearing in the study is given in the accompanying table. Range of Motion Subject 1 2 8 4 5 6 7 P ce treet wand a~ Ai, [Pre-treatment [31 53 45 57 50 43 32 Fost 2 precl sent aot | Posttreatment | 32 59 46 64 49 45 40 Aosye of vue fim Let denote the mean range of motion for the population of all physic therapy patients prior to treatment. Also let jz. denote the mean range of motion for al! physical therapy patients after ultra sound and stretch treatment; and let jg =. fy ~ fg. Assume that the population distribution of differences is approximately normal. Do the data provide sufficient evidence to conclude that the treatment increases the range of motion for patients? 72 wart fe het Mh, < dh, CClarm) He the null and alternative hypotheses. qe Ay = MU, - M,, £0 eo Mg re Ha’ Ly 42 Uff. farfegl ii. Calculate the standardized test statisti laiw fr 7B C5 , Bye RO2FT,Y fe d- Ay _ngsaeo ee —— Ap alta 2-023 WS iil. Identify the rejection region, using a = 0.05. = = Be 3749 tn he ee) ABQ= fiject Wo if £Z- 1-943 ore A Go iv. Draw your conclusion and state it in the context of the probleet? “1443 phswved £= - 2-39 fo Aetet He. <— . / bane s Luh Lviduce fo piper! Whe Cain.