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Unformatted text preview: EC 41, UCLA Winter 2009 Name (print) Midterm #1 —1/26/09
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 non—integer answers to 3 significant digits. e.g., 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 answers.  Be prepared to show a photo ID during the exam (e.g., UCLA ID)  You may leave when tinished. Do not disrupt those still taking the exam, 1. Circle T for True or F for False (2 points each)
1) T [email protected] categorical variable takes numerical values for which arithmetic operations have meaning. T/br F In the demand for murder example, time series data for the 1.7.8. suggested that increased use ofcapital
puTtishment would reduce murders per capita. 3) T 0 ' F/IData l‘roni a back to back stemplots such as incomes for unrelated American and Japanese individuals can he
used to create a meaningful scatter plot. 4) T o®ata on price, income, or wealth are typically skewed leftward (downward) toward smaller values. affair F In a standard OLS regression OH! on X, we assume X is measured without error but that there may be errors
in the measurement on. 0 r F le and Y have the same standard deviations, sx T S\', then it will be impossible For either the h‘.cstimated by
r ression on on X, or the bl’ estimated by the reverse regression ofX on Y, to have a value greater than I. 7) T [email protected] a standard linear regression of Y on X. the squared sum of the horizontal distances between the estimated
line and the actual X values is minimized. 8) T or®30r the regression of Y on X if X is two standard deviations above X then the corresponding predicted value on ( Y) tnust be more than two standard deviations above )7 (assume the correlation between X and Y is not l or l).
@r F An event A and its complement (AC ) can not be independent (assume P(A) is not equal to zero). [@r F Each parameter has one true value, but each statistic has a distribution ofpossible values. 11. Brieﬂy, clearly, and correctly answar the following 10 questions (3 pts. each) 1) A sample has five observations: 0. l, 3, 3; 7
a) What is the sample mean? ‘ b) What is the sample variance? 0) What is the sample standard deviation? 9.58%" a w lllll‘ ‘. s 'n ‘11" o w 3 ‘ “1'! ‘ t are n?
)ho (.h In (1 n) d tlllLll to non p d to me ,2 U P LID _ .5 o. 143 ° 969’ b how much more in % do men earn com mred to women? 0) what is the average wage for all 300 people in the population? pp ’ w .. 7,5." 0 ll)
L(9>03+,3M{£ly) * f‘lg " """ o . , r7— , 
3‘90 1: 5 % 3) Consider the following 3 (x,y) pairs: (2,1); (4,4); (6,5). amsider two different little to explain there at] linel:y=2+(.5)x andline2:y=2+(l.5)x X Y \n \n 81 81 9'1 ___a)_Whioh line is a betterestimate by our ordinary least. squares _cr_it_erion? (“Bath lmes me own/“agate! had) 5mm "‘3
"\_—Ll.rt_f ball/t have saw»; 5%? ' f
b) Is eitherline theordiitai‘y'l'eaSt Soﬁa(es t'egi‘es'sion—line? A 9 _ t I ..
015‘ \l ’ “3‘ + x: .%é.,_33 “m9 29:“ " i’ﬁllﬁ‘i; '2: < Ll l bell" to m u— . . 5 "' . ..‘ ' .
4) A test for disease X gtves a “false posaittve“ 2 x3 of the time I a) lf20 people are tested, what is the probability that. none ofthe ’20 test. positive?
?0 A;
C Ct to c . bl 7 e : b) If 50 people are tested, what is the probability that‘l e ot‘the\50 test positive? “9)” = ,36Lll7 é‘.’ 35m; gag/353,. c) What is the probability of at least one false positive if5( ﬁftested? é ’3 A j}
 : 0
I, 3ng (.62593 ' 5) Three values ofx are l, 2, 3 a) What is the sum: ELM] ? g 4 6 7L 9 :_ I Q
b) What is the sum: 2:13 ? 73 ’l a } 3 1 O, c) What is the value ofthe exponential: exp{0} = e0 ? [D {It 6) a) Roll a red die and a green die. Let A be the event that the number ofspots showing on the red die is three or less A
and B be the event that the number of Spots showing on the green die is more than three. Are events A and B  4. .m.._ i) disjoint, ii) complements, iii) independent. or iv) none of these three? (circle correcl answer) b) lfyou draw an M&M candy at random from a bag. The candy you draw will have one ofsix colors. The probability ofdrawing each color depends on the proportion ofeach color among all candies made Assume probability of Brown — .3; Red —' .3; Green = .l; xange '~ .1; Tan=.]‘, then what 'if’tl'i‘éﬁirobabi’ljty"ot‘aﬁfellow (the 6'h color) M&l\/l?
‘1\ P ‘* l'fl : :1.._/0 ’0.) c) Event A occurs with probability 0.3. If A and B are disjoint, then—what is the rla'i'i'g'é’ér possible values for event B? \_ o ant/2R ./ 7) Brieﬂy explain the difference between stock and ﬂow variables and relate this to the relationship between income
statements and balance sheets. 3be pawl m lane ‘3 hﬂidﬂﬁslrri
I i r l iv PM" {if $2 Mimi} ’6 a?) H") ill61%"; '5’ =3 [rt/,5 U3”; "51;, {"3 i fr: y'r.’
." e f! I).l .' n ‘\: “I; b_:'.'.' ,r i? It > .
tutu“. It} Mfgy i 8) A supply curve is estimated with annual time series data.
a) What are the "individuals" or “cases” \
/wr< b) What are the two variables? ﬁ if _
Pt;  ‘ _ \I i L “5 Eli
0) Which variable is usually considered to be the “independent” variable”? [ns‘% 9) Class is graded on a curve with the percent ofthe students with the following. grades: 20% A: 2_0°/o B; 40% C: and 20% D grades. Overall score. " [the 10 students are: l, [,2= 2. 3.3.51.4. _l , 10.
a) What is the average score? I i" "“x
b) What grade would someone with the average score carn‘? g) .’ x"
____.' c) What grade would someone with the median score earn? 0/ \\
_/ / x..__ﬂv 10) a) lfa fair coin is flipped 5 times, what is the probability (before the first flip) ofﬁ heads in a mu"? (I V r :", ﬁgiii ‘Ogi?§ ﬂicﬁiicii b) lfzi coin has been flipped at times nd the result is 4 heads, what is the probability (bellire the SI" flip) ofa heads on the
5"" flip? f. l
‘ ' / “r1:
q... 74 1) Assume test scores follow a normal distribution with population mean = 700‘ and populatiori standard deviation = 80
a) What is the standardized zscore corresponding to a raw score X z 800? gig/J. 7g! ,1... ( 00 * ' W
“‘3 13} :20 .2 . '2 IH. Clearly answer the following questiorls. Show your work (10 points each, 50 total) 1'“ f I
.r~»"“‘*~."‘\ ' b) What proportion ofthis population scored below 800? < Z/ a }
l' "d' " c) What proportion ofthis population scored below 500? magi/061 _ ., «3:2 " a
Q, .. ,2 5' l .4“: @005 g, SUM a) Draw a scatter plot by hand above to the right b) Fill in the blank cells in the above table. '\._ c) What is the sample correlation coefﬁcient (you may use the formula on the last page your calculatorudr both). #— aun 3‘5 32;9 . M; V?” 6'  3"Yg.2.;. ’4‘ [email protected] 1.1252 15.97 a “L 0 d) What are b0 and b1 f0? the regression Y 2 b” + le (use the formula on the last page, calculator, or hut.8 h,:&_rl.!,‘3"> 1:? '5 r4 bl: 2,: %v'«:~a? taxt ‘ 5‘ ‘ , ...__ h ,/’—“'x
td;\i'h\¥: :_ Be Lax 3‘ "’/ {I
a. 5 t “gt'w
H—_._______,.
A I
e) What is the predicted value on when X = O? \/ : '" . 2: SPF“9 : — t 64x
 / l
 When X = 2'? A "
\ ': ' " ’ h '
/ 1:2 .5 "is": ‘3 l, R“: Per Capita GDP and Life Expectancy y = 0.3353X+ 67.134 78 R2: 0.5678 74 .
72
70 . Life Expectancy 68 . . .. .
56 .. 64 .. . .
0.0 25.0 30.0 20.0
Per Capita GDP, 1000 S 5.0 10.0 15.0 35.0 3) Consider the above scatterplot for data on GDP per capita (X). andwmale life expectancy at birth (Y) for 23 ()ECQ
countries for which data are available. Note the chart indicates the linear trend as y = .3353): + 67.134 u—I—u._._.........__.....—  n M X: 19.7; Y = 73.7; 5x = 6.9; and sY = 3.1 a) US. per capita GDP was 30.6 thousand dollars, What does a linear regression on 0_It X pmﬁijet. as the U.S. male life
. . a '\
expectancy? Compare this to the actual US. male life expectancy of 73.9 years. _ ‘_
it /.'> 7 :3. a A .\ . ’H t k ,... ..
\/~ new «W 4 "' 7 x. (3‘?! j} l
b) What is the value 01‘ the residual. and what does this imply? ’ h _ xi}
t . . l‘ 5: I?" ll‘ 3 kl: I. s r,';..:,. ... I i’ W! dual l‘ltitm'iit‘i l... ' m Wino. that i w i ..: r . l tr . _whﬁti W a i:' l at {l w {l ’t" T' c) Interpret .r2 . What does it imply about the linear regression of Yon X and variability of Y about its mean? When we
use this interpretation, what are we assuming about independence of x and/or y?
tan in in l 't/ ‘tt 1/ a bait it .F}r.<;b‘fﬁ" ' '
. ’ _u .h .I '= . 1,: . N ...
01 it}; west:
“l ilrf. l") l W“ Cit’3“; ' I ,— _ r .' _.. 3' .._
y “i 'f .fairrfhi'fr‘. "t: Era}! '.‘ a L ‘9 if!“ ' Ii ". ' d) What is the predicted male life expectancy for a country with per capita GDP = .6.' thousand $ and how many
standard deviations away from the average of‘ 73.7 is this prediction? " ' ' f 7 g q a: i} r; it? 7w e7 W; + .3353 (Mb? “751.:_7_3_,T4 3’. .t frat ‘ .. e) The estimated equation tor the reverse regression of X on Y is: = 105 + 1.69(Y). What is the predicted per capita
GDP For a county with male life expectancy of_7_6_.f$_y_ears. and how many standard deviations away from the average of
19.7 thousand is this prediction? 7 A! "; LEE 1. it}, P} _
A . mam. _ k 3 R
_ é. a n. \ I! I P I, .7 _*
V“ l0"; 71].!)‘91ijé‘53 ] 23"). “lll a 31 '_ r u _“_,._..n D Relate your answers to the term “regression towarﬂhe mean.” _ : " Z .I ’ y I_ y “ y
Mm V. t at '. t I fit“: * i a ‘ ‘7 57 “5 4? Vi"? ti "‘ 7 i, "\ ' I _ r 7"? Ir  I \f i ‘K I»! 2. l 7 34 {a x} \ f",
a l l, A
4) Let X hourly wage for a sample of 14 workers. The values of X are: S, 5, 5, 5, l0, 10, 1 l8, l8, 20. 23,2141 50
a) Clearly write an ordinary (not modiﬁed) boxplot to the right (Q
and clearly indicate the following on your diagram. " ‘ CG
. . _ {fl} t
Minimum Value — §
l‘irst Quartile, Q. g 1” _
Median I t; in _ Third Quartile, Q3 ? r; ‘ a _ ' tag 1 7 q
Maximum Value p U. __ __
J! lvl 3 S,
_ 13‘ l I] "
b) What is the lntcrquartile Range (IQR)? 2 g "t: a? 1‘
‘~ —/ (an _ I : Kn” S
U  ‘ 
0) Are these data Syl'lllllErt/lle'UT—Skewgd? _  —~ It'sk '*d, ? a . . R '
* W W sliruafl l r '3 hi m pl ~ . ., _  \qu I r at 1 1;}
. l ;
d) Write a stemplot oflhis data below: e) Write in a histogram below as done in tllejﬂl l aw ’l I!“ {1513 I:
__ \ h . ‘i _ (J 0 8‘ Q ‘2’ g o a s  H
I; . 'I ’2
Li 5‘“ l
tn . j "\H  6
f/ ".,______ 2 I 1
PL) 0 ‘ .___ 0 10 0 30 40 50 I come a“.
5) Consider the on—time arrival data for two airlines, Northeast Air and Southeast Air for ﬂights from LA:
Destination City: Detroit Houston
Airline: On—time Delaxud Total On—t'ime Delayed Total
Northeast 2400 600 3000 800 200 1000
Southeast 900 WC 1000 2700 300 3000 a) Aggregate this data and ﬁll in the table below:
Flights to Detroit or Houston _ Orrtime Delaved Total
Northeast 63 ’2 9L} QUE] Cl (iUli Southeast ‘2, 6;? U fl ill} “ill/if)
 I l
b) Compare $116 overall percent of flightsﬁn—tili‘IC—"lfor Northeast Air and Southeast Air. é
r  l
‘20 0h M 7qu ‘lhl IiiW‘s
\ 33 ‘ .. I. . l? ; l}
t it“) $313 a 2;: mgr3. \: F. Db ft)
. z .. b . 5E?  b
". Q “L ' ..' 01 . .. "' {i
a r L. l ' m 0 L) at”? r_ q I!" .20 ﬂopLDoes the above data provide an example of Shnpson’{PamdvxP Brie ﬂy state why or why not.
lr ' f a i m; a” '. 3 '3 ' l \
\Nll I_ Hlﬂtllbltlylwﬁi ; Li. ‘tﬂlll Ill/l {later 0.»:A In " " 2:". [it‘suflﬁwﬁutf‘rl (latte : Mm“? Em" We wait: w * wr r a; liars
‘\ .\ ‘A . ,4 {i "‘ 1" I
{Lull‘tﬂal‘ ('8 U ’0 0h "3"“? la' Tl: " Formulas: 1 ( _)2 _ nZXY—(ZXXZY) : 1 : xI_§ yx_;
vim—(m«gm(w g 1,022..—
nZ(X2)—(ZX) 3.. Probability V
..
‘3 :. Table entry for z is the
area under the
standard normal cuwe
to the left of z. o % iv o‘sﬁiéﬁﬁﬁ" . \ My. 2 :.:¢. ‘2 .. a. “Mt:4 _ .«:..   _ ' mate 'A "
Standard normaE probabilities (CCntirHHﬁJJ 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .567. .5714 .5753
0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141
0.3 .6179 .62 I 7 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879
0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224
0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549
0.7 .7580 .761 1 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7352
0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389
1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621
1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319
1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441
1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633
1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .976] .9767
2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .991  .9913 .9916
2.4 .9918 .9920 .992 2 .9925 .9927 .9929 .9931 .9932 .9934 .9936
2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964
2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974
2.8 .9974 .997 5 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981
2.9 .998] .9982 .9982 .99. 3 .9984 .9984 .9985 .9985 .9986 .9986
3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990
3.] .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993
3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995
3.3 .9995. .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997
3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998 ...
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This note was uploaded on 12/06/2009 for the course ECON 41 taught by Professor Guggenberger during the Spring '07 term at UCLA.
 Spring '07
 Guggenberger

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