Final Exam Solved - Introduction to Statistics - Fall 2006 | STAT 1222, Exams of Statistics

Download Final Exam Solved - Introduction to Statistics - Fall 2006 | STAT 1222 and more Exams Statistics in PDF only on Docsity! NAME 2 Hi G29 (Dues Tee, Mag yt) [dit STAT 1292 _ WINAL EXAM SHow Werk on ali Problems stable extra pages 1 tf, . . Lensare 4) Thing a race, a sample of five sports cars has & mean speed of 173 mph. ‘The speeds {in miles per hour) of four cars are: 187, 181, 176, 153 I@F+IGi th) tHs3 +? - 193 Find the speed of the fifth car. ay a) 165 (o108 ©) 70 a) 17Le) 178 1 LOE HIGIFL FE HISSt?Z= Sr1tZ ho, 15 $65- (187 4181 +176 + 183) = /168) = 865 Use the following information to answer questions 2 and 3. & ‘The closing prices (in dollars) of a sample of six stocks are recorded as: 20 16 15 12 16 3.2 2. The media se of this sample is 10 TNedian Price oO. 1S SATE 1S > middle obuke ah l2 b LW? oo) (O35 e) 15 tr points Che Axvange ja imvwnsing ord: 3-2,10,12,15,16, 20 Cheba Median = = 12415, r 43s 2. 3. The standard deviation of this sample is a) Q4L —b) 5.28 O79 a) 27.92 e) 33.5 Ke CorgrserrtlorZ2 1, &? 205IE as a & Use the following information to answer questions 4 and 5 The scores on a statistics test were normally distributed with a mean of 78 and a standard pe $ deviation of 7.3. Fd 4. A student who took the test was randomly selected. The probability that he scored between 75 and 95 is closest. to 2 (Kt) jm , cg g, A+F-2 (Yosso2 b) 3409 c) 9901 d) 8721 e) .5312 PC te ex cas) > Plas- tae « 15278 ye P(- +41 6 B42. 33) 43 RB =e 5. The lowest test score a student can earn and still be in the top 20% of scorérs in Che 4 3 class is closest. to a a) 80 b) 82 Or d) 86 e) 87 Sle -20\ 7°22 ehaded hen 222, te 2 hea left fe 22%) ary — (amen lft sf 2e =79) Step2~ x: 2 + (84) 7:3) fe 4401 - 3404 le} 2 X2 MtEr 72 | » ga reo yal STAT 1222 FINAL EXAM ne FALL 2006 6. We want. to estimate the mean repair cost. for personal computers (PC ). How many PC vo Peet repair costs must be included in the sample if we want to be 99% confident that the sample mean is within $15 of the population mean? Assume the population standard 2 deviation is $24. “7 Somple sire Pow de an (2) a4 b5 7 @ (1) eer 2S FS, A224 g., F »Erts Feromden- tv Sample Sire probes ye (*: See eg ye Aluotys voitwd fo next hidhan integer. Se) tthe 7 Use the following hoe mation to answer questions 7 and 8. The mean height of a random sample of 45 women is 64 ches with a standard deviation of 2.5 inches. ‘Vhe data set has a bell-shaped distribution. According to the Empirical Rule, 4 7. which of the following is true about this sample? a r BEGG H ber 64 {a) about 95% of women are taller than 59 inches. a - oe rth GBR th HATS (Davout 95% of women are between 69 and 69 inches tall. ly = (c) about 95% of women are between 61.5 and 66.5 inches tall xe LA 94 (d) about 68% of women are between 59 and 69 inches tall. x1478 =6 Db, e about 68% of women are taller than 61 inches. 2Y Fon f creek GSI 1, bie betwoer %- LA 8. the approximate mamber of wornen im this sample whose heights are between 61.5 66.5 mches is: bles fo 66S = Ke 4 fonts a) 40 b) 89 c) 35 (Y 31 e) 26 Proportion = +6 Fie Nunebene ovoportion) (Totoll 9. Earlier this week, Linda took Biology and Statistics tests. The Biology test had a mean #6845) of 63 and standard deviation of 7. The Statistics test had a mean of 23 and standard =. 306 deviation of 3.9. x 3 Lina scored 71 in the Biology, and 29 in the Statistics. Find Linda’s z-score for each test and determine in which test she did better. (Cisne z-score were 1.14 in Biology, and 1.58 on Statistics. She did better im Statistics. (b) Linda’s z-score were 1.14 in Biology, and 1.53 on Statistics. She did better in Biology. {c) Linda’s.z-score were —1.14 in Biology and —1 53 on Statistics. She did better in Statistics. (d) Linda’s 2-score were --1.14 in Biology and ~1.53 on Statistics. She did better im Biology. (ec) Linda’s z-score were 19.14 in Biology and 13.33 on Statistics. She did about the same in both tests, ac 2i-b3 . [1424 Seve Biobgy * ; Steve Tee Calis + 9 a By wuparivg ¢ score, Linda lid betty ju 54 be Hes STAT 1222 _____FINAL EXAM FALL 2006 18. The standardized test statistic z is closest to: ne 6°, l Ange Samy a) -02 b) 28 O “138 d) 138 e} 18 ge xo x ae 1s = 10 rhe “2 B)é 19. the p-value of this test is closest to: ”~ - ~le 2422 a) 0237 b) .0162 ce) 4286 d) 5714 Ce ).0838 ‘— loft-taifed tert, Ao Pz (Wor fof Ze 1-38 20. At @ = .05, your the decision is: LASH ve, 2--1-28) o~ (a) reject Hy and accept H, since the p-value > a _ og 283 ( fail to reject, Hy since the p-value > @ a. ¢) reject Ho and accept H, since the p-value < a jes ection Oude ‘- {d) fail to reject Mo since the p-value < a ej of “f ns é He if P Z A (e) none of these °B 0828 ye Os vo 1 obo nol get o- Use the following information to answer questions 2land 22. A. researcher war the hypothesis Ho: p= 0.23 vs AH, :p # 0.23. Given that the sample statistics are n = 200 and p = 0.27, NP lwo - tule of tert. 21. The standardized test statistic z is A a) -127 hy) 127) 188d) a fe) 134) FF f fon # na ‘E PY/n (aucet 22. At a = 0.1, the researcher's decision is: Zoe S447 (a) Fail to reject Hg because -1,96 < z < 1.96 ne (b) Reject. Hy because z < —1.28 5 ech or (c) Reject. Hy because z > - 1.645 ar et ) twe- tar a (d) Pail to reject Hy because 1.645 < z < 1.645 reer > te 05 (c} Fail to reject Hp because —1.28 < z < 1.28 ~< Borie peeeeiple® DHan of ) -t, 9 by 2/64 i] pyeck om bef (on = a. ~ Pb 4S . [dejec hor puke “ (eject He if 2 — 164s 0 17 F645 STAT 1222 Ce FINAL EXAM a. PALL 2006 23. In a random sample of 19 shoppers at a grocery store, the mean amount spent was $28.15 and the standard deviation was $12.50. Assuming that the amounts shoppers spend on grocery are normally ee construct a 95% confidence interval for the population mean amount spent. . 1, =16f , emall sample ., x7 2° 2.60 (a) (22.53, 33.77) : T. Pow ah: Z eh ep (22.13, 34.18) Ye oe.“ MEX Ie OA (c} (22.15, 34.15) aA "Tr Wels -\et - eo , (d) (26.86, 29.44) f GVA 1By Ea 4s - 2-10] 20101 (e) (26.77, 29.53) tee 1 ak ZL tbls + qosees (12°50) _ . 2Ge1S - tates Rite] ZLYLS 2 US 3M TG Areal estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood was = 18,250 with a standard deviation of s, = 1200. In the second neighborhood, 10 randomly selected households had a mean income of Z = 17, 500 with a standard deviation sz = 950. Assume normal distributions and equal population variances. Two Aadwple | indipendut , Awa Aample » pop: Vax. equal (KG) - M- Ay) f Grae: RE age) BE ea 24. The test statistic is be oe nee Wit yey we a) 1.536 b) —1.232 c) 1.600 a) 1.636 e) 5.437 4 ~ $0) ~ (0) (16 250 17 8P0 =f = t 6003 E71) 1290 * LlO- dase fe at y2450n 2 . The equation bf regression line between the variables x, and y is given by 7 = ~ 3x -+ and the correlation coefficient is calculated to be r = —0.95. Which of the following statement(s) is (are) correct? 1. The variable y is positively correlated to the variable «. IL. The variable y is negatively correlated to the variable a Ne il. If 2 = 5, one would predict that y = Lon ; Xr Ye -B(s)t 2 IV. if ¢ = 5, one would predict that y= ~13. U~ ertSt2 {a) Only [is true 2-13 (b) Only IL is true (S (Only Il and IV are true d) Only J and £V are true {e) Only TY and Jil are true SAT 1.222 . HINAL EXAM AALL: 2006 PART fl FREE RESPONSE QUESTIONS 1. The table below shows the weights (in pounds) and the daily caloric intakes of six adults Weight, o | 1027 M8) 1257 1491 155 | 180) Calories, y | 1500 [1576 [ 1800 [1720 | 2000 | 1880 | n=6, Sor = 829, Shr? = 118,579 SS y= 10470, Voy? = 18,447,700 Say = 1,467,940 fa) Calculate the correlation coefficient r between the weight and the daily caloric intake of an adult. - (824) (710.4 Fo) Ay: p> He pO Find the standardized test statitics. 4 aX Find the er point and identify the re At awit 4 | twe tailed beak ole vf Stat your decision: [lef ec | He if L fj e 3D wo L. 26364 p 2-122, ae Prey € et H fa (c) Find the equation of a regression line. ye wk x4 b, me nsey~ (erléy) £ (1467 440) Beok7e) = F4bT Fo Qdid 2 wn exe ek ‘| [gages N % “yg (uged~ (824) oe Ge LELS (e) Lo préder the daily caloric intake y if the weight (d) Use the equation In “part nal’ s “~ ~~ Vege . . pa Tes Sie (Ge 28U5 (136) 4 jpig13 4s 1 = 1 topess yy