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Unformatted text preview: EC 41, UCLA Fall 2009. Name (print) Midterm #1 — 10/19/09
TA: Name & Section Time__  The normal table and useful formulas are on the last page ofthis exam.  Only pens, pencils and erasers may be used, this is a closed bookz closed note, exam.  Students may use a calculatm‘. but nothing that can access the internet, and calculators may not be shared.  Write noninteger answers to 3 signiﬁcant digits, 6.13., 333, or 3.33' or .0333  This exam consists of 10 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 ansuers. 1. Circle T for True or F for False (2 points each, and 2 points for going to the correct room to take the exam) Use for the folloiving two questions: for the In a class of25 students, 22 students had grades between 7’! and 80 (both
endpoints included), and three students had grades between 9! and 00 (both endpoints included). l'or these data:
Chmha. . . Ifl [‘3‘
1) T 016*) The mean must be betueen T1 and 80. J: lJZ) 3’ Ely7)“ If [’2' eagf S [X E 2,351, 5:) YiQﬁpr
2®>r F The median must be between 71 and 80. [email protected] F Benford’s I.,a\\ (used to cheek accuracy Ofﬁnancial documents) implies that the probability ofthe first digit
of numbers in financial documents is more likely to be 1 than 9. ‘H——'— '4) T [email protected] Flatland is divided into three regions: West, Central, and East. “the unemployment rate in the three
regions is 3'5’3, 6%. and 12% respectively, then the unemployment rate in all Flatland is approximately 7% sahon
5) T [email protected] hi the demand for murder example, the professor argued that that UFOSHIZIIILll)'Sl\ was superior to the tune
series analysis. since “all else" can be. held constant. 6) T or® A regression can be performed using only the information derived from a backtoback stemplot.
7) T [email protected] A standard OLS regression: )9 = 170 +131 X is of“X on Y.“ 8) T or E if X and Y have the same standard deviations, s}, = sy. then the slope ofthe reverse regression must be the sam" as l/sl ii" lflll” forwarl re ression: b‘ ' 1.." b _R . '
e I <}L;11L'e t g I l “L fpllﬂidfql tie) {)Zf ny
warm Gt“? ., . . . .
It [he ran um variable 7, = X"Y and sample correlation eoeltieient 0, then \‘tuiance 01 Z ts the sum efthe
Variances of X and ‘1' (o;_"‘ ox) =' of) y M whiz/ll [‘Ciq GAMEWM
will in" T2 M: II. Brieﬂy, clearly, and correctly answer the following 10 qugstipns _(3_ pts. each)
1) 3) Draw a “Time Plot” with year on the horizontal '— a:»;is. Show Price with x’s and Quantity with 0’s on the PE J [a Q "‘\\
vertical axes for the following data. I H / / \
Year Price Quantity Income f: l / 9' /}‘ \
20l0 2 2 8 ' 4 , i j.
anti ’t 5 I.“ 1’ . ’ = ’
2012 5 6 14 r ; (9% 3L /
l
i i . s   _ . /’ CIRCLE. CORlxl, )LLW. x...» 3.1133,,» b) P and Q are «fern/13w ‘NIZGATIVELY associated. c) prlon Vertical and Q on hori7onta axes, these three ('P,Q) combinations would be on a demand curve:
Tim; 0 w MW 33? MC
2) Consider eightvalues from a sample ofa variable X: 5; l; 0; 0; 2, 1. ﬁx
a) What is the sample mean of these 6 observations?  n 7 f— {V j;
if r i 2 e 5 2» ‘3 ? b What is the sam le variance of these 6 observations? . __  ‘
) p {3% J 5g % b c) What is the sample standard deviation of these 6 observations? ‘3)‘}( [email protected] 3) Using the data in the previous question: ' ﬂ 4 a) What is the first quartile, Q1 (usi a: tet’s method)? "l 1') U ,\ l l 1) b) What is the median (using the text’s ethod)? . i ' 3
M ﬁlm/i : 0i e
2;
C.) What is the lnterquartile Range IQR (using the eats method)?
tag: 4) In a population of workers, 25% earn $20 and 75% earn $30 per hour. a) What is the average wage of workers in this population? ‘ ,Mx : Jiféal i~ {73/357} : 5}],er M“ b) What is the population variance of the wage for these workers? q; 933» (ﬂu2733i": $73“ (33 I» 27531 : lLliﬁbMt Llubg‘ib” 3 w c) What is the population Standard deviation of wage for these workers? Ux L lile ’lghﬂ VQi r) it W .
5) Consider the random variable X with the density curve below.
0 10 . """"""" " .. «.4 a ' — whee isthéc who e—ieize+v£hn+iee called? i. il‘il 51E}? ‘ ' ‘ W [’5’ .. a .4. b) Suppose random variable Y has the same distribution as X.
Draw the distribution of W = X + Y to the right:
(label the highest and lowest possible values). C) What is the probability that W is greater than 5: P(W > 5)? Péi; >§ : a I g L__Y
O 3
l 2
l 4
2 3
b) What is the sample c) What is the valueo ' d slope coefficient for the regressw . I _ ' I : — C, +b1X ‘ .
i b we ﬁttiﬂvh‘ii‘ll’i’lé Mamet! ~ gram/31:9 (1k? ﬂa’g‘ W aim Mi 7) For a particular population, assume test scores follow a normal dist ‘ tion with population mean = 50, and population
standard deviation : 8 .~ 5’56 "577 [é
a) The standardized z—score corresponding to a raw score X = 66 is v ' “T r... '2 8) A test for disease X gives a “false positive” with probability .02 (2% of the time) and the results of each test is
independent of previous results. I, w . _ M a) If 100 people are tested, what is the probability that none of them test positive? {C74 it 7 I.
.a . b) If 100 people are tested, what is the probability of at least one false positive? in M252 ; .t’ia‘ias ’3’ positive? YES 0 (circle the correct answer) "HP/m 9) a) Suppose the true probability of Bob getting an “A” in any class is .2 (20%). Assuming his grades in class are
independent of one another, what is the probability th classes and receives two As? 2 9 El? it dis/'1“?th {9sz LIL/g7 b) What is the probability that he takes two classes and re ' es no As?
'  . a?
[‘1] cg (p 2 c) What is the probability that he takes two classes and receives one A? (rea ' Asandboth AS) _ lgq v6 Z i”, c) Does the above Fawn provide any information about the chances that someone with the disease will test Retained Earnings;
,, Wealth :> >ggjéé/{g III. Clearly answer the following questions. Show your work (10 points each, 50 total)
1) The following are three observations on two variables X and Y: away 7343» it 592157 56%“
d) Report the slope (b1) and intercept (b0) of the estimated regression line of Y 2 b0 +
._ \ S' c k i. r“ v' ‘ W r‘
law 3 2331? :lxlaececﬂb 3 i5“ I 61/2; ‘5: A 2) a) Fill in the table below. The estimated least squares regression is: Y : l + 2(X)
X Y Y b) Verify 2 (pry ' a “’l' _, ~ 2» ,
g I 2&9. “7 ' ‘ " 
l l (, . _
l .' if.
is above in art b is minim1ze y r inary Least Squares regression? “Wit—W d) Find the value of the coefﬁcient of determination: r2 = Z ~ 1—” / 2 (Y — )2 N: 2% : ﬂ:
Lil/e; Lil .e.._= W: ‘.=—— ._ ﬁﬁhiizrté Bl f E? a) What proportion ofthe class has a score between 70 and 80 (report to 4 digits). P(z<.§5~ P(Zé ﬁfl‘e P2<,5“*[t —P(i<.5:( ; .gqi§~ﬁ~.bfttﬂr .50] {$139K Use Table/1 to give a “'comtlrmlire” aItchr, rounding offto be .mre the Student is at [Hurt in the (0p X%; e.g., [/8
places a student in the 10p 10.] ’36; and 9 the top 9.9%; then 9 is [he [Owes] score placing person in “(op 10%. " b) What is the lowe 't integer score that guarantees a student is in the top 15% of all student ea. 5—99
75 +0.04 wt ‘ BSt
PLZJ . (‘15de m 2,
c) What is the lowest integer score that guarantees a student is in the top 85% ofall s I ent scores.
7;  Luz )w ($1.7 #9 as: w.  nil/mt 0,) ﬂ
w d) What is the lowest integer score that guarantees a student is in the top 30% ofall s O 8 S“ .52, 55 .
lilJ 5429 70:4 79+ ' 53 0w 2 80' a e) What is the lowest integer score that guarantees a student is in the top 70% of all t dent scores. 73., (9.52 ‘319 : 661.9 . : ,2, 'ent scores. ll 4) Pay; gender, and major ofa group of recent graduates is below: , Men Women
Major IIighPav Lew—l’av Hiyh—Pav I.o“~1’;ly
lLcnnomicx 200 50 9 1
Other 50 100 40 50 a) Aggregate this data ﬁll in the tahle helmx:
Hi hP' LowPav Total b) Compare the overall, aggregate er‘ ofworkers with high pay for Men and Women. 7.51) in qu
Y F ~,— __ ._
imam LIL?) w W” H?!) a e) Compare the percent of workers with high pay for Men and Women separately. for Economics and   4 ‘. n t ' ‘
majors. E;an ._ 200 L _ 3M .fwn ﬁlm '2?) ' 90 ’0 N MW tart“) d) Use the above data to brieﬂy suggest that woman do not face an earnings disadvantage in comparison to men. —_ ._..__. \. ﬂga’lgwggw‘ Vt talk/rt— Pity/59rwa )9 LWWM CW {Ll lugl4 My)  .————'—"—— e) Use the briefly suggest that woman do face an earnings disadvantage in comparison to men. ore/J'ttcahid ~ ht lop/WW 0? W? M limit pill/M11)?
€> H166 is mm» Mei/Wt I" plume/Mama PUMP Wow/IF"! “479’th 5) Consider two independentaandom variables. X Probability Y Probability
—l .8 0 .7
l .2 2 .3 a) Find population mean/and population standard deviation of X ( a ' AM ; eWl t 352}: tart: 1 4 ti? 3 (w ~~tlZBM (2° :5inle “1 Obl{é?ll—(a§elti’l zigzag WM; : b) Find population mean and pultion standard deviationf% (ﬁnd variance ﬁrst) I’MV: 7Q}! 3 D it; 4
v3: a team i (bulbs r; C)Z:X+Y. (FY 3W: Write a table to the right showing pos ' :
values on and their probabili is e)W=XY. 0 Find population mean and population standard dev' ' I o ‘ W (ﬁnd variance first) MW; Jaw/la, : .‘ig : . it; Quilfﬁétfyé‘iir‘i ma = ma QETW 1‘ 37M ‘— anZ l Pam/a)
Piles/3M am pathway, Wk L? Q diwgﬂw \ Awr 96279145le ME: 4&6ij {(zijk we)
 5‘5+.38 +1? ‘ (9 7; . _ ‘ ,
0}; @Mm Jamiest 4 5mm
=37; L 94 ;S\L( : Ta: Km  i~21b357§ 3’ 1.22 /qu= 462%; PM?” 1&0] .7Z h.£2 kw ;@
(NZ: ('3 «4.29, W4 [4 “(26.1; 2 _ L 32(qu : (—Lsxzét/S A (23362; (z‘szw
: £77745} Loqu 7L ,6776 1 (WWIILIE: llmggzwé :3 Table entry for Z is the
area uner the
standard normal curve
to the left of z. YIN: ., 7.3,“: uih.:::+:w~ A
Mi i’lm’iizeu ggwﬁazmumb .50th
.5478
.0235. 13293 i . .168. 133103
.6450
.6844
.7190
,?5]?
3823
.8106
.8365
.5599
.5810 .9102. n“;t7§l§0"‘.i.y '25.“
G\ 2'  90 ..w..,,,2,»M\ s mm «mm» . .9 2 7'9
.9406 2
a
i
i.
z
2 .991, 6
.9936
.9952
.9964
.9974 '1
.99S6
.9990
. .9993
.9995 .9995
.9995 .2‘9?
.999? .9995 .. .1.  2 1 Wanﬁll 2 r w. I .._»u
erm. . ._ , r U
bl:w_ﬂ:r§i b0 Yb)? rich—(XXV 5x Population mean and variance of discrete random variable formulas : ,uX = lepi 0;, = Z (x1. — ,u)2 pi .9920
. 9940 .9948
.5996: II. .9943
.9957
39188.
In): w n5 ~I Kg ‘37,; 'K) 0\ Ln 4.: DJ lu >— A
av ‘.i L») U) L»: I'm) FJ [~41 Pa.) lv’ lv’ l\J in; l) Ex) — —* '—\ r— 'r—4 — — >— H b.) b.) r——0 L») WW“ W. .wawmwwwxmmw M. W......,,.«.W..mm «rmawwwm‘owwxh'xnw MmeN Dispersion of linear combinations of random variables: 2 w 2 2 2  2 2 2 _ 2 2
0a+bx “ b 0X 0X+Y ‘ 0X + 0r + ZpOXUY UX—Y — 0X + 0y _ 2pJXUY ...
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