Intro to Statistics Final Exam 2006: Questions with Answers | STAT 1222, Exams of Statistics

Download Intro to Statistics Final Exam 2006: Questions with Answers | STAT 1222 and more Exams Statistics in PDF only on Docsity! ST ER BEY HHO STATI222 Final Exam May 4, 2006 The following is used for questions 1, 2 and 3. A sample of cieht. resistors of a certain type resulted in the following sample resistances (ohms): fe ~ Uy (ip § yh post fron ‘S / ve v Ihe bess fi 40, 43, 39, 35, 37, 43, 46, 37 f the qui dd le perhen 1 Bind the median of the sample. wee we hk DD OH Z 36 3S, 3 ty 3 ry ; (a) 36 Ye (b).. 37.5 c)/ 39.5 ‘ ° ane A a q4heo d) 33.5 e.dian 5 Ate (e) 43 2 2 Find the standard deviation of the sarnple. (a) (b) 98 (c), 12.25 (@) 3.742 fe) 3.5 3 a the ast quartile of the sample. a, t Anker ly LH of {a) 38 & 4s jake W b) 39 . fx tc. - mild le p ose fi ((a) 37 4 a - S Te) 40 $ - Gi! STAT1222 page 20f 15 May 4, 2006 Use the following to answer questions 4, 5 and 6. In a survey of 250 juniors majoring in psychology or communications at a large university, the students were asked whether or not they are happy with their majors. The following table gives the result of the survey. Assume that none of these students major in both areas. Psychology Somunitnications “Total 4 What is the probability that, a randomly selected student from this group is happy with - oe of the major? ? ( Lappy} (b) 25 (c) 32 8A On 5 Whaé is the probability that a randomly selected student from this group is neither happy with the choice of the major nor is a psychology major? OP PL itor Laphy sor Papel ajo) (ce) 32 ? [ rhe p py ancl [i ‘mn HiCAL On tajov ) (d) At (e) 60 = 38/rse = 414 6 What is the probability that a candomly selected student from this group is uuhappy with the choice of major or is a communications major? (a) 82 _ , : fe ) (eh. 89 P (uh ap hh Hw (Communicators «Y e = TLunls bP y) t ?/ fata mru yi catrons ) oe Pl uurhahy oa of Cwm ntyniith oun ) = So ob Tse -~ Fon be STAT1222 page Bof15 May 4, 2006 13. Suppose you want, to obtain an estimate of the mean caffeine content in a cup of coffee correct. to within 3 ing and with 80 % confidence. Find the minimum sample size necessary Lo estimate the men caffeine content in a eup of coffee. Assume that the population is normally distributed with a standard deviation of 30. 9 : 97 ae “ye a DF _ - - 2. ym Ee 8, oe?) me (MEY [pppece “= 3855 ~ . a. 164 a = 30 sy oe Those + . . = -Gh (d) n= 664 163 4 (e) n= 2401 a aud, ‘a ° tg cund up The following is used for questions 14 and 15. A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a wedical examination during the past year. A random sample of 200 elementary school children indicated that 18 of them had received a medical examination im the past. year. b = pb Ve, ot fion whe have Eucejee d Medeat éxaw 14. Bind point ostimate for p and also construct. a 95% confidence interval for p. (a) 09, (04, 14) Be IS ong Zan 46 ye i (b) 9, (01,17) P Goo” “° ty a = Gl (c) 200, (01.17) “A “a ps b t te (a), 200. (08 , 18) pO ed L- ae 09, (05 , .13). idem, ef5GS 15. Using the information from the “above 2 PLoat 1-4 #97294 hone ne, find the minimum sample size needed to estimate the population proportion p with h 99% confidence. The estimate must be aceurate Lo within 02 of p. (a) nei fe vem Uh. Above ey (b) nm Ab5 | cat male fe 4h & STN yang / ¢) mse 1358 Td) n= 2936 Aw p> 04, He 9A (e) n= 2401 aay + ne pw) > (on(-w/?  _page 6 of 15 May 4, 2006 The following is used for question 16. Starting salaries of 50 college graduates who have taken a statistics course has a mean of $42,786 and a standard deviation of $8,912. aoe 4k FBL, vie Oo, BoB aie, Lange vi dandih ; 16. Construct a 97% confidence interval for the mean ‘starting salary. Also, port the critical value z, corresponding to a confidence level of ¢ = .97. Diyfpe 2017 ¢ (4005105, 4520.95), Q17 ARCL RE KR a B) (9857.15, 4451288), 247 og “ (ec) (40315.72, 15256.28), 1.96 eRe AAS THE ey (a) (40164.48.45407.52), 208 perth M428 107-6 (ce) (38146.26,46128.74), 2 ' 17. In the context of statistical hypothesis testing, a ‘ype I error is edd 4 (a) Failing to reject the mull hypothesis when it is false O05 te OES < 135 0b Is ae (b) Failing to roject the alicrnative hypothesis when it is false Rejecting the nulf hypothesis when it is true (d) Failing to reject Uhe alternative hypothesis when it is true (e) All of the above STAT1222 _ page T of 15 _.May 4, 2006 The following is used for questions 18, 19 and 20. Randomly selected n, -= 55 stuctent cars have ages with a mean %, of 5.9 years and a standard deviation s of 3.7 years, while randomly selected my + 60 faculty cars have ages with a mean _ of 7.1 years and a standard deviation s, of 3.6 years + wo 4 twp ple, ua depe so pencluct, lange 18. 19, 20. dis, ple Choose the correct hypotheses to test the claim that faculty cars are older than student Denote by x; the mean age of student cars aud by gy the mean age of faculty a) Faeully Cane olde: Manna Ka)? Hy: ja > py versus Hy spy < ple , - Lo. tp ote iy iy & vorsus Hy 0 Py < Fy udeud . “he ve es “ (c) Hy: pa < py versus Hy: pa > bo Age f Stu ie CMS Aaah d flys poy pty versus Hi: pt A [he en drag? Tew y Saif t j (e) Ags ty < py versus If > * J 2 ot fy SS fla SUS Flat fl 2 Ha qe: JA, c Ah, Hoi Ay My My Ah eM, Find the value of the standardized besh statistic. (a) Yo pes (b) be (XP) fata) 4 (c) wi 2 t ‘ (a) -L-760 OE ae Bae 4 Ue pols” (ce) 4.285 4. Ny 60 Find the rejection region and state your conchasion at a = .OL- < ~2.779; Decision: Fail to Reject Hp. 3; Decision: Pail to reject fo. (a) Rejection Region: z Co)" Rejection Region: » (c) Rejection Region: z < 2 : Reject Ho. (d) Rejection Region: z < 2.36 : Reject Hy. (e) Rejection Region: z > -2.779; Decision: Reject Ho. left j uiled [ljeck Woh ee 2-32 1GGE % = 20 3B, Be Porsd STAT1222 ——spage 10 of 15. May 4, 2006 ‘The following is used for questions 27, 28 and 29. Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 230 yards on average. A random sample of 177 golfers show that their mean driving distance is 230.7 yards, with a standard deviation of 41.8. 27, Sel up the nul and alternative hypotheses to test. for the designers belief. (a) Hy: p< 230.7 versus H,, je > 230.7 ap MV Rh Age Mor Tha (b) Ho: pv 230.7 versus H, : ye -f£ 230.7 . I oF (c) Hy: > 230.7 versus Jd, 2s < 230.7 . Z 20 Wee AA 7280. Cap Hy: je < 230 versus Hy, + je 30 ~? ied -failed (c) Ho: we > 230 versus fH, se < 230 28. Find the vatue of the standardised test statistic, (a) 7 —p Meltt;, Ye peek, ge bs, (b) .223 [ mje samble (c) .125 , we (a) -7 {e) -.125 29, [ind the P-value for the above mentioned test (a) 0871 7“ {b) 5871 (c) 0228 (a) 9772 (SY 4429 STAT1222 page 11 of 15 © - May 4, 2006 The following is used for question 30. ‘The equation of the best fi¢ Hue relating the amount of bill (in dollars) « to the amount of tip (in dollars) y is i = 180 ~ 2.70 ‘ ap) 7 tf : Revert 30. Predict the amount of tip if the amount of bill is $ 70. Q 4 0 (a) The predicted amount. of Lip is $12.60 ~ I (b) The predicted amount of tip is $ 10.50 @ The predicted amount of tip is $ 9.90 (d) The predicted amount. of tip is $14 End_ of Multiple Choice Section STAT1222. page 12 of 15 May 4, 2006 1. The table below reports Wie ages (in years) and the number of hours of sleep in one night by seven adults. sleep, y m=? Yoex 387, Soa? = 18563, Soy= 44, Sy? = 296, Soey = 1916. (a). (2 pts.) Calculate the sample correlation coefficient r between age, m, and the mumber of hours slept in one night, y. We ery lenley < ¥/I9b) ~ (23744) - 4499 i ues {En (b). (5 pts.) Test for significant linear correlation between age of an adult and the ninnber of hours slept in cue i, hy an adult at a = .05 Hy: Pe oO Hp 2 PeLoS. Ide ect Ho if i Lo DSF ot i 22e4l pF 6/7. 2 Uy Decision? feejel Ho fenge