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

Download Final Past Exam Solved - Introduction to Statistics | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 FINAL EXAM FALL 2007 Consider the sample data 1, 5, 2, 4, 0, 3, 4 i y5 42 tage O34 Y i ST2 +g Se AIRF i. The sample mean of this data is closest to Rod os wv a4 bd) 2 Od an e) 3.16 y 2. The sample median for'this data is Avitine iw Fudenouny ovdet- é, 2, 2 ? 4, 4, Ss a) 4 b) 1 c) 2 d) 3 e) 3.23 — Y Mon at 3. The sample standard deviation for this data is closest to fax f qe, ide fb ie a) 467 b) 100 Jigs 4) 216 2) 3.23 posi har ) 4. Old Faithful, located in Yellowstone National Park, is the world’s most famous geyser pose that the distribution of the "waiting times” between eruptions of the Old Faithful approximately bell-shaped with a mean of 79 minutes and a standard deviation of 14.5 minutes. Approximately what percent of the 2 waiting times between eruptions fall in the 50 to 108 minute of map tye fod (a) 68% (b) 81.5% 4} (c) 19.5% = fay j95% 50 hws aq G35 10g ) gy a Me ie ¥ @) 2.5% Mei fo A ger AE Use the following information to answer Questions 5 and 6. The next two questions refer to the following table of data collected from a survey of a company’s employees concerning their feelings toward a proposed revision of their pension plan: 7 Blue-collar White-collar Decision Managers workers workers For 67 32 11 lig Against 63 18 9 46. . \. i30 SO 10 \z0eo 5. If an employee is selecked at random, the probability that the employee is a blue-collar worker is a P ( therellaa} = 130 pH yg gM Gi) yo Plrbewln)= 150 “0 77 200 | XY aon = To eee 6. If an employee is selected at random, the probability th that the employee is a White-collar : { \ worker and is “gainst the proposed revision is re t shite te than 2 eats wif 18 32 18° : Ihe § Agjmcwe — = — 1 i 9 79 °) 55 ° 200 i 200 a wile gellin # Agee a - eee Talal # Hh PLY VT gad 4 =H 43 -, Sle zu x Me &29a4 wLgsq | 222244 — ~°Fiya \ oF 10 pa (HH age begs iG 5 30 1 Bs = a PETS & Ol -4- 443 | 7636 74 2 “LEST "eels qooaed 3 LHate 2%. STAT 1222 FINAL EXAM FALL 2007 Use the following information to answer Questions 7-8. Scores on the Standard-Binet Intelligence Test (IQ) are normally distributed with mean # = 100 and standard deviation o = 16. 7. People with IQ scores above 132 are considered to be” gifted”. What is the probability that a randomly selected individual is gifted? x7 T & Ntoe as PV laGled\ _ Vex >132)2 Plzr (B2-ue ) Te (c) oo = Fl 27) . (d) .9772 co beg Aft of 322 ab 9FF2 (e) 4772 Peete 8. In order to qualify for membership in a certain organization, one must ‘have an IQ at the 90% percentile. The minimum IQ score required for membership in this organization is closest to Weed. do difewwive x value [es x that 1S {a) 118.5 aw the hy 4th 4p th frreeih le pl. m1 SEebE Doane fee HO 0 (@) 90 S febe: whee BTN, (e) 120.48 ep2- Ket Bas loot (28) (yg) = Zar ag Use the following information to answer Questions 9-11. The following table gives the probability distribution of a discrete random variable z : z T-l; OT 37 3 Pla éxsd= Veet ¥ lke WEE tee) p(x) [0.2 1.0.21 0.5/0.1 The AG 2 lw Tastes 22 P( xo) F P( k= 2) < ° he -s ~ 4, 9. on a) a) 02 (07) 9 0 d)10 @)1 10. Fig the mean of. Adz o XPER 214 (du b) 0.25 c)18 dd) 09 ¢) 15 11. Find the standard deviation of zx. a) 1.89 b) 0.0 387 d) 11 e) -11 L Pe E(x Per = pdr 1.44 STAT 1220 FINAL EXAM FALL 2007 Use the following information to answer Questions 19-22. Many people sleep late on the weekends to make up for "short nights” during the work- week. The Better Sleep Council reports that more than 60% of us get about 8 hours of sleep per night on the weekend. A random ¢ sample of 350 adults found that 235 had fk about 8 hours of sleep each night last weekend. “SL 7 T We i he a3 ly we m A bow 19. Set up the null and alternative hypotheses to test the claim that bee than 60% of us get about 8 hours of sleep per night during the weekend. Hh . Hy: p= 60 Hop =.60 Ho: p= 60 ove than 66 1. (a) e (b) i) Aa: p< 60 Aa: p< 60 A: p # .60 Mew ~ -¢ Ho: p< .60 Ho: js = 60 . a Jape Desk peje 60 Hew to find b ? 20. Find the test standards atte for this test. fut of oS °, 23s h acl y he ol 4 pa lees, ~ (a) 1.98 q= ae ~ Hb - Ae fh = 23, Ny , (2.73 “R ae 350 . (c) 0.67 [ 6 6) (eH) uy pe by polls pied Propet on (d) 2.95 “S55 =z ag ° (©) 248 t= 24266 ~ 2-43 YUol-pe ex 21. Find the P-value for the test. _ i id. . j oom 7. es & te (a) 0.0121 a 5 Mt fale ef Te right i bsetvedd 2 (b) 0.9977 (¢).0.4977 a 446 AP Sheed ayy’. [- +9968 (5.0082 — 7 (e) 0.0523 ark PS +go3z ~Dobseved 2 22. At the significance level of 0.05, which of the following is the correct conclusion? (a) Fail to rejéct Ho since the P-value 3s Tess than 0.05 eee Lien full (b) Fail to accept Hy since the P-value is greater than 0.05 (c}, Reject Hp since the P-value is greater than 0.05 Us ~ Ve ‘Reject Hp since the P-value is less than 0.05 i oF mater wh vi A pe (e) None of the above. Akko } (eejec Ho if P K ok Use the following information for Questions 23 and 24. Suppose that we are.interested in comparing the academic success of college students who belong to fraternal organizations with the academic success of those who do not belong to fraternal organizations. Cumulative GPA is used to measure academic success. Random samples of size 40 are taken from each population. The sample ee are listed in the following table. A, Ade Number | Mean | Standard Deviation Claim: ‘ Fraternity members | n, = 40 |Z, = 2.03 $, = 0.68 © fa liffevasd | Nonmembers Ng = AO | Zo = 2.21 $2 = 0.59 At 0.05 significance level, test the claim that the GPAs of the two populations are different. Ve Awepley | en {| mee pom “e , use 2. 23. Choose the correct pair of hypotheses to test the claim. , (a) Ho: ty — bg >0 vs Ha: py — py <0 (Oto: ty — z= 0 vs Ha. by — bg #0 (c) Ho: py — tg SO vs Ha: py pg > 0 (d) Ho: p44 — ty > 0 vs Hat fy > Hy <0 (e) Ho: py — My =9 ve Ha: by fy 20. 24. Find the value of the standardized test statistic. (a) 2.32 Yo (b) —0.32 iy hte Two- busted ; aw ep hb (185 | yg Pe Clabes Atul) ee (a) 1.26 oe = less? Pod i (Ps Jerbes = 106 , Do wel weject Ho. 25. The equation of the regression line between two variables x (independent variable) and y (dependent variable) is given by 7 = —3z + 2: and the correlation coefficient i is r = —.95. Which of the following statements are correct? I. The variable y is strongly positively correlated to the variable z. (1) The variable y is strongly negatively correlated to the variable x. ey If « = 5, one would predict that y = 17. © Q--3 (9742 ® re S (Wilts =s, one would predict that y = —13. oJ ao Dyas lS (a) Only I is true {b) Only I is true (c) Only II and IT are true. (d)_Only I and IV are true. () Daly It and IV are true, STAT 1222 FINAL EXAM FALL 2007 | PART II FREE RESPONSE QUESTIONS 1, Medical researchers have noted that adolescent females are much more likely to deliver low-birth-weight babies than are adult females. Because low-birth-weight babies have higher mortality rates, a number of studies have examined the relationship between birth weight and mother’s age for babies born to young mothers. The following data on x = material age (in years) and y = birth weight of baby (in grams) summarizes the results of such a study. we} 16 17 18 18 16 19 17 16 18 19 y | 2289 | 3393 | 3271 | 2648 | 2897 | 3327 | 2970 | 2535 | 3138 | 3573 n=10 De=170 Vy = 30042 Sa? = 2010 ry? = 91785351 Say = 515,600 (a) Assuming the existence of a linear relationship, find the equation of the regression (best fit) line relating ytoz. y= lol sis 660) — fie (Bony —— (ite) (Bees), _ 246-15 be y - ve . Ge: 3004) 10 (240) — 1707 fe 30% oo 2040] lays, oy ; “Pieo) 2 oe [92 2 (7 [3 Ye LES X = 169 YS uF “A 8 be ~ieg-4s ae nt —— (b) Find the standard error of the estimate. aan 7 Pb es- MPM Gi7as3s1 ~ (Mbs4s ) (00 Je 24518) Ve C1sh009 v-2 V arrears estnyannnrpisnnnrannne-imonrnns ~ (O- 2 4 = TES 939 4 (c) Predict he: average birth weight of babies born to 15.5-year-old mothers. We DASE 5) — Mpyse 2340S (d) Construct: a 90% prediction interval for the birth weight of a baby born to a 15.5-year-old mother. sex 13h. 3064, df 10-2 ~ “6, tee 366 ; Kot iss cue $9 tae (TH LL 2634+ 9S — <9 4 268-05 + Y- Biolvosnay fads BI pet wa \ yet 10 (2410) - an LL E34. 034 6g¢qH7 4 3S COR os + Ae 7 ZOE 4 154 42064 4 0°44 he él . [e233 30h