Statistics 10 Midterm_1682828889573

/ Stats 10 Lee 2 and 3: Midtern1 Version 1 Introduction to S tat istical Reasoning Mi chael Tsiang UCLA, Winter 201 8 Instructions: You have 40 minut es to complete the following questio ns . This exam is clo sed book. Yo 11 may use only one sh ee t of paper with handwritten not es . Non-graphing calculators are allowed. bnt no other electronic devices are allowed. Good luck! Academic Misconduct: Any pot ential violation of UCLA's poli cy on acade mi c integrity will be reported to the Office of th e Dean of Stud ents. All work on this exam must be yo ur own. In the Special Codes section of your scantron, fill in a 1 in the K column. UI ~ . '( , .,.,., e 12p.,.., CK) (Turn over when exam starts) l

.,t;:; ") 2 Stat s 10 L ee 2 and :~- ;-. \· - -- ---- ------------- --- - ------ --- -· ...... :.· 1, 11 , - ---:.:! Mark your answers to all multiple choi ce questions on the scantron provided . Any answ ers marked on these pages will not be scored . Probl em 1 The ti111 c yo u wa it in line to order a coo ki e at Diddy Riese would best be modeled as what type of \·a ri abl c? (a) N um e ri cal va ri able (b) Catego ri c al variable Problem 2 Coo ki e flav ors (chocolate chip, sugar cinnamon, oatmeal raisin walnut) at Diddy Riese would best be modeled as what type of variabl e? (a) Numerical variable (b) Cat egorical variable Problem 3 Th e number of waffl es Les li e Knope orders from JJ 's Diner would best be modeled as what type of variable? (a) Numerical variable (b) · Categorical variable Problem 4 Th e distribution of blood types for a sample of patients wou ld best be visualized by which plot? (a) Boxplot (b) Histogram (c) Bar chart (d) Scatterplot (e) None of the above Problem 5 Th e relationship between the number of waffles Leslie Knope orders and th e volume of whipp ed cream she puts on them would best be visuali ze d by which plot? (a) Boxplot (b) Histogram (c) Bar cha rt (d) Scatterp lot (e) None of the above itR :!. - p:11

I I I I I Stats 1() Lee '.2 and :1: :\ lid t,, 11 ~ - - - --- - --------------- --~- - - - ----- .:_:_ " The followin g information is used in Probl e ms 9 a nd 10 . A class has 10 st11 dc 11 h;. T lw scores 011 the latest test were: Pro bl em 9 88 70 g_Jll 10~ 83 8 U0 79 , . . .~ , 'tl•S . ~ -? \\ hat 1s the mterquart1lc ran ge of the test sc01es. (a) 2 (b) 3 @r 'L ') v\ $' (i 1 q 7 ~(U) .? I ? 1 L 2;s 8-1 (d) 11 (e) 22 Problem 10 \Vhat is the median test score? (a) 82 @82 .5 (c) 83 (d) 83 .5 (e) 101 l V (Q ( Problem 11 Sherm Bian ca l ana , owner of Sherm's Ic e Cream par lor in :t\hmcie. Indian a; recorded inform ation about his customers over a one week pe ri od. For each customer. Sherm recorded the ice cream flavor order ed (flavor pr eference) and wl wt her the pPrsou wanted it in n com' of cup ( co n ta iner preference). Chocol at e Vanilla Stra wberry Cone 120 lGO 20 C up - 10 0 lfi lG \Ou \ Vhat proportion of c ustom ers who ordered a cup 1 want ccl d1ocolnte ice nenrn ? - lfo (a) o .:33 _,., l DV (b) 0.25 (c) 0. 75 (d) 0.40

Stats 10 L ee' ) · 111c l 3· !"I'd - ' ' · l\ I t<.' l'lll 5 Problem 12 Supp ose' d ata ot ti , .· . , . . pri ces shm\ ·. ti . t ti 1 . . . 1 ll JJI I( ( p <'r g ra in ul saflron is rnlk cted. A hi st ogram of th e S Ir\ IC l 1s tnlJ11t101t i 's · ·] I . . . . of ff . $ · rot1 g t Y sy 1111n d rH' a11rl 111111n uda l. T he m ea n pn cc per gram sa ron is , 11. 48 and t ht ' st· d· · I 1, · .· • . . . . . . . ff · , · ,lit r1 1c < ev 1atlu1t 1s %2.12. A local g ro ce r, food Ami St uff , 1s sellmg sa ron for $8. !J!J !) Cr nrt \\ !! . t . . l . . . . . . • . . h < m. lrl . IS t IIS (>J'I( '( ' Ill sta nd ard l!lll1 S! no1111d to the n ea rest hundredth. \\ onld this pncc be cow; iclcrc<l ,11111 s 11 al or not? ( a) z = l.l 7; This is 111tu sw 1. ll y expens iv e saffrou. (b) z = 1.17; This price would not be unusua l. @z = - 1.17; This price would not be unusual. ( d) z = -1.17 ; Thi s is unusually in expensi ve saffron. (e) Cannot be determined from the information given Problem 13 If the correlation between two numerical variables is close to 0, which of the following are true? · j The scatterplot could be a random cloud of points. I , --;, -_ · 1 lr"r. The scatterplot could be nonlinear. ~JI the points would lie along a perfect strnight line, with no deviation at all. (a) I only (b) II only III only (d)h nd II only ~ , II, and III Problem 14 Many medical researchers have suggested that the inciclence of ast hma is higher in city-dwelling children than among those living in the s uburb s. Some reasons pro vided are that city-dwellers are exposed to more pollution, more indoor smoke, and oth er possible co ntribu to rs to asthma. However, researchers at Johns Hopkins published a st udy t hat fouud that th ere was no difference in asthma rates between city children and sub urbau chilclreu. Thi s st udy is an exam ple of which of the following? An observational study controlled experime nt (c) None of the above .

St ats 10 L< ' C' 2 ,111 d :{ : :-l id ti'l'III 7 Problem lG Chu<J s<' tlw l H' sl . t , .. , , . . . • , . . · 111 < i p1 1 t.1111111 !JI il l(' rn l11 <' iii r - 1n t lw < · u11t< 'xt ol the data . (a) 1\IJ 011t 11 .:i'X ()f of tit,, I· . 1 ·, .· • . . . . . t ,ti ,l u \\ It '1111 u1u ' st ;1 11dard d1 •v 1at 1011 ol th <' r q.>;r<'ss1 u11 l1m '. Alio nt I. LG ½ oft h< ' total variati,rn i11 l1i <'ar l1 011:it< ' is <' X pl a i11 rd li y t lw pH. ( C) A bout. 1 l. G Vc of 1 he ) 01J se rvati u11 s fall , HI t II< ' regr <' ss ion lin e. (d) Pn , cli ct ions of bi carbunat c bas<•d OJI tlw r <'g rrssiun Jin< ) \\'ill iil' corrrct i11 alio11t I J .S% uf the cas('S . (c) Abo11t l I .G% of the total variation in pH is ex pl a in ed by tl ie level of bicarbonat e. Problem 17 Th e correlation coefficient is approximately - ~-3 7.77 @-o . 339 (c) 0. 339 (d) 3. 39 (e) 11.5 Problem 18 Which is the best interpretation of the slope? (a) Well water with an average pH will have, on average, -37 . 77 ppm of bicarbonate. (h) Well water with an average pH will have, on average, 432.15 ppm of bicarbonate. fc f)icreasing the pH of well water by 1 will decrease the le vel of bicarbonate; on average, by 37. 77 \J pm. "0) Wells with water that is 1 pH value higher (more basic) than oth er wells have, on average, ', 37.77 ppm less bicarbonate. We lls with water that is 1 pH value higher (more basi c) th an o th er wells have, on average. ' , 3 7. 77 ppm more bicarbonate. Problem 19 Can we use the regression equation to pr edict the level of bicarbonate for well water with a pH of 5. 5? (a) Yes, we can always make predictions once we have a re gT ession equation. (b) Yes, we can make a prediction because the scatterplot shows a linear relationship. I, (c) I'i o, we cannot make a prediction becau se we ll w ate r with a pH of 5.5 is outside the range of ~ - o' ur data. We would be extra polating. (d) No , we cannot make a prediction because th e correlation coe ffi cient does not equal l.

Sl ,\I :-, ] () L <'c :z and :J: :\ l idt l' rm Tl 11 • fnllm\ in ~ l1 ist o~r: 1111 is w .; 1•d in l'rnl ,l1 • 111 s '.W , 2 1. a nd 2 2 - _.L \ 60 \ ;,,, u g; 40 ;:::l 0- <lJ 20 0 LL_J_ ·]_ 80 100 120 140 160 180 Probl em 20 Wh ich of the following boxplots represents th e sa me data as the hi stogram above? (b) .. ........... --- [D 80 100 120 140 160 180 8 1 0 100 120 140 160 180 (c ) f 1 - -- -:~ , I: ITT 80 100 120 140 160 180 80 100 120 140 160 180

Stats 10 L ee 2 and 3: l\ Ii<l term ][) Pro hlc111 24 \ kn \\ · _\: 111 r l'pu rt s tlwl thrrc is a :.\·rry strong, n ega ti ve , linear as soc iation" bet we en the n1110 11111 or 1 110 1w .\· sp (' 11 l 011 11 cig li bor h oo cl po li ce patrols a nd the nu mb er of crimes committed. I s i111p li e~ tl wl If we " · er e tu li t a <r gr ess ioo lirr c hc tw ec rr the rrru nbcr of c rim es irr a neig hb o rh ood and th e a 111 01 111l of 111 0 11 ey spent 0 11 po li ce patrols in that 11 eig hb o rh oocl , the slope wo uld be clo se to + l. 1 f we were to co mpu te the correlation co e ffi ci ent be twe en the number of crim es in a neighbor- ' \ u1 oo cl nn d the amo un t of money spe nt on po li ce pat rol s in that neighborhood, it would be close to + l. (c) If we were to fi t a regre ss ion lin e b etwe en the number of crim es in a neighborhood and the amo un t of money spent on po li ce patrols in that neighborhood, the slope would be clo se to -1 . @i f we we re to co mpute the correlation coe ffi cient betw ee n the number of crim es in a neighbor- h oo d a nd the amo un t of mon ey spent on po li ce pat ro ls in that neighborhood, it wou ld be cl ose to -1. Probl em 25 C on s id er the scatterplot below. SC ATTER PLOT 100 90 80 70 60 l' ' >- 50 40 · 30 l l . 20 l I I I I • 10 ... . ' I 0 . 0 2 3 4 X 5 6 CHWIRU12 .DAT I - -- '-"'-' v\'hi ch of the followin g are corr ect in terpretations of the relations hi p be tw ee n X aud Y ? ~ t app ea rs th at an in cr e ase in X ca u ses a decr ease in Y . II. There is a st ron g co rrelation be twe en X and y . III. There a pp ea rs to be a strong m, so ciatiou be tw ee n X and Y . ~ I o nl y II o nl y (c) III o nl y ( d) II and III o nl y ~L 11 , and III