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EC 4],'UCLA Spring 2009 Name (print) _ '
Midterm #1 — 4/20/09 I
' TA: Name & Section Time  The normal table and useful formulas are on the last page of this exam  Only pens, pencils and erasers may be used, this is a clOSed book, closed note, exam.  Students may use a calculator, but nothing that can access the internet.  Write noninteger answers to 3 signiﬁcant digits, 6.3., 333, or 3.33 or .0333  This exam consists of l0 True/False (20 points), 10 short answer (30 points) and 5 longer questions (50 points)
 Clearly write answers on this exam. No points are awarded for illegible answers.  Be prepared to show a photo ID during the exam (e.g., UCLA lD)  You may leave when finished. Do not disrupt those still taking the exam. I. Circle T for True or F for Pulse (2 points each) lngmi/i A‘ 1) 'I' o.'\notl1er name for “variable” is "case." when observations are not on individuals. zlﬂm' F Another name for “qualitative variable“ is "categorical \'ariz1l)lc."‘ 3) T or®ltavorage earnings are $50 for women and $70 for men, then average earnings (stall people is $60
4) T OI@ The "Budget Deficit" is a sleek variable. SQ” F its, .> s,. it is impossible. estimated slope ofa regression of Y on X to be greater than one. AM) T“ .fl/lIlI/(ll'lvi‘; '/ 6)®r I" Making statements about samples.§ven known population parameters is an example of deductive reasoning. r ‘ 'i iers "L3 L1 si a C!‘l11)kt‘ ' s " s ' 's la, is 5 1"5 r '5 ie i i. I tore ‘resisa " re: s 7 1 ll iutl ha\ n ll 1 eton a ummal Ian I th unnnm tit] t s 1 l ‘ ltlll n t UIL
e.________,.  . ______, 8) T 0r®llie sample mean. _\’ is a measure of central tendency which minimizes the sum ot‘the ﬁisulnte \‘alnes ofthc deviations ot‘X, li‘mn .l‘.’ _
9) T or®lhe main point ul‘thc “demand for Innrder“ example in class. is that there is convincing ex idcnec that
increasing. use ol'eapital punislnnent reduces the rate ofmurdei‘s. This sl'0\\'s e\ en potential murderers: rationall) respond to incentives. IUD 10@r l" correlation hast on averages is usuall) higher than if we use data for individuals. PM”? l‘r’f/ a/WQ‘UL/ II. Brieﬂy, clearly, and correctly answer the following 10 questions ( pts. e 1) Consider the random variable Xwith the density curve below. height = 0.5 0 2 b) Suppose random variable Y has the same distr
Draw the distribution ofW '— X i Y to the right: greater than 2?
(F"\ { Vim 2) .\ deck OH? cards has 13 hearts. ‘ _  i I ,. I
a) What is the probability that two cards randoml.‘ '3 J 3  1 _ 5' drawn with replacement are both hearts? (5 Z 2
h) \\'hat is the probability that two cards randomly ’3 ’2 A t I 2 Q h EV
diauii without replacement are both hearts? a — Li f _ l 4 . D S c) What is the prohzilxilit) that tor too cards randomly : W812 : * ssﬁgg 23 g, ‘ 55.0] ll N
‘3
b. ' ( . 3 ~") “17‘
dt'il\\tl without replacement iicitliei die hearts. 5 ' .2; assume tcm event: toiiowa normal distribution with population mean = 700, and population standar deviation = 90 a) What proportion ofthis population scored below 880‘? _ \\ Z (lottn, t‘ﬂp'r'tci‘ E
z= W17”: 2 13049arle/Bée’zl : AW/z v we r L t;
b) What proportion ofthis p0piiation scored between 790 and 880? no ' '\ {m l><< 66th ~ P r <7.< 2i r PC3423 W203 351%??? ‘ .l 1) ’3’
if _ a _ L't..{/ 4 :r____,. c) What pro onio@this pop ilation scored new 8 0‘? ___ m ’ I P z» 93°“,‘4’0: l — Pﬁz< tel : l ~ fl§2€ 4) Consider the following 4 (x29) pairs: (0,2); (1,2); (2,4); (3,4). Consider two different lines to explain the relationship:
line l:y=:0+2(X) and line :'y=2+(X) A
a) What is the sum ofthc 5t uarcd residuals for line I? b) What is the sum ofthe squared residuals for line 2'? ll
2 a? 2..
iii Q) Which curve better ﬁts the data bascd on the criterion for regression presented in Chapter 2‘? and 20% D grades.
) What is the average grade point for students in this class (4=A, 3=B, 2=C, l=D) .ZﬂJJAerl t.4/2Ji.zm : .5»! t L? m :  meals '—\/“
Overall scores for the 10 students are: 9 10, b) What gade would someone with the average score earn? e) What grade would someone with the median score earn? Iqalmr ‘ L>© “IN S) Class is graded on a curve with the percent ofthe students with the following grades: 20% A; 20% B; 40% C;
A; 8 i 6) A sample has three observations: 0, 0, 30 a) What is the sample mean? ~. .
. X I I
b) What is the median? I. I ‘@ _
if _ c) What is the sample sdtvanilgdgeviation? etutz+ﬂwzfi7w2 # Llé?‘ I72) ' Z
'2. ﬁijTliree values ot‘x are—1, ], 4" a) What is the sum ofthe squares? Z:IX‘2 ? l l l ‘l l b : @ R
Z t 2 .‘ '7
b) What is the square ofthe sum? [213,13] ? 6 F @ ‘= . 3
c) What IS the sum ofa constant c: 2H 0 ? @ 8) In Chapter 2, in order to estimate a regression line a derivative is taken ofa function. Write this function in a form which includes 'the two variables which this function is partially differenti rith respect to. T I ver, think about
what is minimized and how to we minimize it (Realize slope can be eithe b or b; and interee ta or b0)._
/. W. . _ . .4 2 h m h ' fri;————————_s:1 _‘
QM}! Hull : mm {QMAX}; W am a 9) A test for disease X gives a “false positive.” with a probability of .003 a) If 200 people are tested, what is the probab' _'__ one receive a false positive? 54.52,. tip/e? b) f200 people are te5ted, what is the probability of at least one false positive? All” Hitl’arf'tlﬁ c) If400 people are tested, what is the probability of at least one false positive? I @971”wa [~220065 ~_ 10) In class it was reported that individuals with an undergraduate degree in economics get paid more on average then
those with undergraduate degrees in most other majors. List the three reasons presented in class. [D " premiums [5 Us; “lg? (“9521] W‘grl/ ﬂztfpléyﬂg
l9 " htgl’t pfvptip'l/tu ﬁll prowl Hwa _"'0 fadmd’gglﬁﬁli \ _
lb * HOWE” SatWhat yawn ml l/ltgl’llb/ fentilsz germ/5 III. Clearly answer the following questions. Show your work (10 points each, 50 total)
1) Consider the ontime arrival data for two airlines, Northeast Air and Southeast Air for ﬂights from LA: Northeast Southeast 0 mka 1 I Destination Ontirne Delayed Ontime Delayed
Detroit 800 200 75 25 _ +5
02 _ 29  Houston 95 5 900 100 ' ' ' I I
3) Aggregate this data and ﬁll in theptallle ' _
Flights to Detroit or Houston '? 0) Compare the percent of ﬂights ontime for Northeast Air and Southeast Ai 't each of the two destination): lfyour ﬁnal destinatio ouston and arriving ontime isimpgnanh—xvhichairline would you prefer (if price were the same)?
M \, . . fu E I Uri—F’iw—_T;lj ,Lw . Ct: ELK. ._ , L 1/ ,
“ll ' w. ~ tljl “551” l: "02‘ ‘.Q§ ‘\ had, 14 Pl 1.9"!“ H55?
_ a . I — ' Isisw '
sec 16' . 7g 5&1 tel; .th / 0i will iii/i ' “PM
. H‘a ' 1WD :4, “'1 (l h star3:2 We ‘ l
d) Continue WI 1 te tn ormatren in the previous question. Both atr mEs ﬂy into , ere a tgtts arrive ontime. All
ﬂights from LA to DC have a stopover in either Detroit (for Northeast), or Houston (for Southeast). It is inconvenient if
the ﬂight into the hub city is delayed since you miss you connecting ﬂight. In this case, which is more relevant, the ' aggregated or d‘ : treated on—timc reeo . grﬂyitateyhy _ . _____ _
U53? it!) llam'l—mt {l4 li/U’él will Wit19%? Palm!“ ‘ ,/ ()l' (NHLMtg gt: hf 91’! _'ltl’l’”, HELL; 1 ._,_F——_.._.____ __ 2) Roll two fair feur sided dice (I, 2, 3, or 4, spots equally likely for each die). One die is red and the other green.
8) Let A be the event that the sum of the spots on the two dice is three or less and B be the event that the sum is 5 or
greater. Events A and B are: ii) complements, iii) independent, or iv) none ofthese three? (circle correct (maneg)
2/ b) Let C be the event that one spot is up on the red die, & D that one spot is up on the green die. Events C & D are: an
i) disjoint, ii) complements, iii) independent ,br iv) none ofthese three? (circle correct answer) 2.,
c) Random Vat'iahle X — sum ofthc spots on the two dice. Show th ‘ possible—values.ng and their corresponding
probabilities in a probability histogram below. P \ "— — _
' » l )L Pt Uh Rm...“ (3
_ 1/”) ,; .06? 3‘ xx
' an; m: * "LI ’i/fb : 13):“ "3 The x ‘25 —e“;:»zz_u m: .
_ ’ﬂLE'. 1L: 1sz? 3) The following are four observations on two variables X and Y: Y
c
ll
7)
Z a) Draw a scatterdiagram t0 the right
b) Fill in the table above c) Calculate the correlation coefﬁcient between X and Y. r = j l bilqbg 145% L IN 1mg
tercept (a) of'the estimated regression line on on X:. Q: d) Calculate: 1?: > ; 6) Report the slope (b) a 1‘ 215 Continue Wllﬁ ma trom prewous proBlem. a) Wltfﬁlgtlie predicted value on when X is one standard deviation above its mean, and how many standard deviations w ftgtwt t " 's r ' '7
(/iiJayJ he n;ell;%O:YLIIIS/l:_ p I F5 3} dis}; ‘1 lé‘ t/ult x: it _ 71’th / l l is i t” 2 f; 'lmtr/at‘rl {llﬁlvl’rﬂldélft’é—x)
' it»? VF; _ I I_ I D) ./ lulu/U * l_!_frf’_flﬁ'/
l ill I l!” i a l i ————f ' x
( N w. a t a) b) RepOrt the slope (b’) and intercept (a’) ofthe estimated L[ regression line OFX on Y, and draw the corresponding scatter plot to the right:  t. H L
_ g. f t ttﬁil _\ __
by: r 51;: (93%] ' Ila ' l
a ‘ X“ l: V ‘ ‘%—€Awwt c) What is the predicted value ofX when Y is one standard deviation above its mean, and how many standard deviations
away @the mean ofX is this predicted value? A 
X“)? _ Qatar 3 — 9 7— e_. ' c; _ w
QlY‘Htm ‘ ) l) 'GHQ'EUX X_ ‘ tglll C—Vaiﬁt
22:.” 2/6) \ _ X 4,555 3"! élﬁw/ ill/37533.6 law/ﬂit) $ /t /V —‘ — _ FL“ 5) Scores for two different tests: I,\ x I I "'*I‘l
' 7r]! '1: 7_ J '1' my}? = :97 .9 7
5 5‘ b6 l S’ Q p” TESTﬂl: 66; 87;80; 70; 65; 73; 71;34; 34; 34; 37; n: H
5C ‘5 95‘:_1£§§1§.?_ 0'?sz tr; ﬂFﬁ"? q; 6] { :1 III 6) Write back'Iobgglggjemgplots as in the text (lowest to the highest: for the scores or} these two exams:
__.5 f “5‘ TEST #2: 53; 55; 62; 89; 90; 58; 60; 58; 64; 66 h : (b c) Write sidebyside ordinary boxplots below:
9 83; \ TestIﬂ Test #2
\ w... 100 / 90
4 ’2: 60 quaniles for each: 50 7 Cr Lao WM
d) Write two histograms below with either cowigﬂthﬁDJEﬂ/axis as in the text. With intervals 5060, 6070; 7080;
80QQ;%6W004ﬁW that th lower value is includecLJbut notjhe upper value (6070 includes 60 but not 70). "——._._._ X25 ate—amlami lcient? Brieﬂy explain why or why not. 7 *5 0w fir [Kl Yl {351 it"“xam
ml ‘hfWm/‘r" N“ r /i\
1M_Lr'l’/2 ~ WET/(l if I j /. ...
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