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Unformatted text preview: Economics 41 UCLA Fall 2008 NAME (Print) October 20, 2008
Midterm Exam I. TA Name & section time:  The normal table and some formulas are on the last page ofthis exam  Only pens, pencils, and erasers may be used — this is a closed book, closed note, exam. — Students may use an ordinary calculator, but nothing that can access the internet.  This exam consists of 15 'l'rue/False ? (30 points) and 10 short answer ? (30 points) and 4 problems (40 points).  Clearly write answers on this exam. No points are awarded for illegible answers.  Be prepared to show a photo ID during the exam (cg, UCLA 1D, driver’s license, or son'iething similar).  You may leave when ﬁnished. Turn in both the exam and your seantron. Do not disrupt those still taking the exam. I. Circle either T for True or F for False (2 points each, 30 total). 1f F A sample correlation coefficient may be calculated between two quantitative variables, but NOT two
qualitative (— eategorieal) variables.
a. 2) T eifF‘ :gTime series data on one variable can NOT be represented in a histogram. 3) '1‘ or' F ' If the sample correlation coefficient between X and Y = 1, then the slope of an estimated regression line
of Y on 'X for the same data sets must also = 1. CULT/hr F The US. national “federal government budget deficit is a flow variable.
. Cm d
S) T orf'li‘,:’For all boxplots, the “whiskers” extend to the furtheSt observations which are less than 1.5 quaﬂiles below
the firstl'quartile, or 1.5 tiles above the third quartile.
(9 :2) 6(Tpr F For a histogram with relative frequency on vertical axis, one can not determine the number of observations 2’“ . . . . . . t. 
7) 'l‘ orLE/l'l'he slope estimate for an ordinary least squares regression is “rcsxstant to outliers, but not the sample
correlation coefﬁcient 8) '1‘ or‘ li‘fi'only data from a population that is normally distributed can be “standardized.” 9) T or{F ,iFor any “reverse regression” the estimated sIOpe: b‘, is the reciprocal of the estimated 510pe of the forward
regressioii: bl ) z—y
. . . . . l ‘1 . .
10) T or® Since the formula for the probability of a normal distribution = e a the normal probabtltty
O'x/E density curve is highest when (x—ti) is largest. 11) T or® For three observations: 3, 4, and 5, the sample standard deviation 2 .8165 "t 0"  12) (Elor F s! is a statistic, while Ox is a parameter.
EXT/or F An observation may he an outlier in umvarate analySIs, but not bivariate. 14) '1‘ or®An outlier must be an inﬂuential observation. 15) T oré) If the sample correlation coefficient : 1, then we can be Confident that changes in X cause changes in Y. 5 L51; . ' Ct tr {awfl [Butt ; a .: .. 1.2.  it? It"
1 I I. ,I ._
ll. BRIEFLY, clearly and correctly answer the following ten questions (3 points each, 30 total).
1) The time required for individuals to complete an exam is normally distributed with mean = 56 minutes and a standard
deviation 01'4 minutes. If students are given @116 hour to ﬁnish, find the proportion who will eornplete the exam.
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2) The scores on a university examination are normally distributed with a mean of 50 and a standard deviation of IO. If
the top 16 % of students earn A‘s, what is the lowest mark that a student can have and still earn an A? " Z s t >< — w = f ‘ HZ 4 '\ ' .94/3 .. .. m ‘A' ' p m riot} 2;. 5t: Bette: g, (1: 3) An economies department with 40 all—male faculty which hires two per year, has two retirements per year (each after a 20year career) wants to have 25% female faculty. What willbe the gender ofthe flow of new hires it'this goal is to be met in 10 years? 1 all“, .. . I '
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4) For an ordinary leastsquares regressienline, if x = f , what is the predicted height of the regression line for this
I \. x? '.
i f 5) The average earnings of individuals with an undergraduate degree in economics is higher than for individuals with an
undergraduate degree in business adnu'nistration. Brieﬂy give three reasons provided in class. _— . K ;'
my : . . r.
% 6) Use the regression output below. The dependent variable, W = hourly wage. The independent variable. LOS =
length of service (in months). What is the predicted wage of a worker with 10 months of “service” (experience)? Regression Statistics ’
Coef. I I . .._ ,
Intercept 8.0 . r ' ’ ' LOS 0.40 I .' l4») I 5 T \',‘ fl
7) The diagram below show the number ofjumps for each of 24 student. The variable we consider is number of jumps. ’ _._
"_ ‘ x 'J/  . i ,
x x twﬂlui'” ‘2
x x u'
x x x \
x x x )r x x x I
x x x x x, X x x x/
” . . i 1‘ _ e I
H.....Lt. I I‘: '( . ...! ‘ Jus‘tp's ( ]'.\ / \, F I a.
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What is the median . é ,3 ;and the mode: ' ‘2' ?
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B) In the formula from the text and class: e 2‘ " , what is the numerical value,  (three signiﬁcant digits)?
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, . 2. ' 3 9) What is minimized in fitting an ordinary least squares regression line? Use summation notation. not words. 7 "’ i “A I. . t ‘ d to; 3;: ~11 2 ' 10) A sample othO'ih/orkers are Classiﬁed race. A bar graph of the results is given below, but the bar for blacks in the
graph below has been omitted. What is the pmportigy ofblaek workers in the sample? a) _' _,
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n l l 1 '  1 white black astan other III. Clearly, concisely, and completer answer the following problems. Show your work. (10 points each, 40 total).
1) Let X hourly wage for a sample of9 workers. The values ofX are: 30, 34, 5.5, 15, 20, 18, 25. 18, 28 a) Make a sternplot to the far right (do not “split stems”) and a histogram with classes:
1020,, _20—3Q,ete. below. asdone in the text (with lower but not upper values included). {'1 “*1 J I; _. _ “ II What is the Median? J I _a. ‘I hh—  
. . . , If I . . l r?) r.) I '
c) What IS the First Quartile, Qt? it is} ; Third Quartile, Q3? t ' "W F:  —~_~,
(use text’s method to find Q. and Q;.hin"t: :) L” l ' i '.
d) What is the Interquartile Range (IQR)? _ .; \.
. r,“ 5" '3 1.‘ 5'"
2) Consider the following data on X and Y:
3) Find value 'forf‘m. 0;)»,4 l_ ii) 20%;);1 7.» 7 _ Sump 4 .I_( t _ LID!"; ._ . I 1 . \~. I~..H  . > J? ..
111) (2%) = [2. l "1.60 ‘ l“*‘j.;::..'.;,';i'._,,.,.....;_r' ’ 3 7—2,, ~ .. gr
I t x 1 ' ‘ _ ‘ t m .a g '  '
' xx“ if» F (if)... 24‘ (g r) __ 12L} \(Il )1.” I]
b) Use either your calculator or the formulas on the last page to find: _ t. l/E — l S ""' f :3 Q t i) sample correlation eoeffieient’.’ ,n‘s bl ”‘ H ' ‘3 l ‘93 £3 ' —— it ’ (I) '
ii) slope of the estimated 0L5 regression lin , with x the independent variable
iii) intercept of the estimated OLS regression line, with x the independent variabli .— D I I _ 4' a " A; ho : x; » lax: e—  {ﬁg ~. ?./5 + Halls: true {this .. 3i ConteTa'e'r‘Eicél'6625:1135Elie right. ' I I h ' m' ' " ‘I M
Y = overseas returns (in %) and X = U.S. returns (in %). Mun'p'e R 06000
)7 _ 3 d )7_ _ 4 d _ 6 R Sguare 0.3600 _ an ? — 5 SK _ an S" '— Coefﬁcients \)= Z 2 i H x H Intercept 2.30
a) For the forward regression Y = hL+bIX what is the predicted US 0.90
I x  ’" "x _ '4' — —%————H
mine for overseas returns if é. __ 25 hi ..'6 {3: I if US. returns are: 5 percent? __ I U.S. returns are 11 pereentg r2! 2 :. '3 w 
b)AF0r the “a “P regression X f b’hilb’lYu___\vltat is the predicted value for U.S. returnsif f" I
ﬂ I+ ' t! g! j I. l 3‘ .. . L Overseas returns..,are: —5 pereent’ﬁ ‘— 1 Overseas returns are ll pereentﬁ s l i H 'qu 31")“ K... _  '1' [£4541]  .. "it.
Wj'r'mgaare‘n‘t; p'Sﬁutatiahfassmne test "scoics follow"a'n'ormrtristribntibrr'wini'populates mean? 600‘ and ‘ ' ' "‘—
population standard deviation 2 80 J _, .3\
2.9—0 <2" '1
a) The standardized zscore corresponding to a raw score X = 800 = '3 xii; ‘_’ b) What proportion ofthis population scored below [email protected] % )1 I t. ‘ 1‘ 1 _ ' C? 39 L .1; P I E a
. . . 2St‘’ﬂ " ‘”
c) What prOportlon ofthts population scored between 650 and 800?\<n__ ~E~ 9;) ‘
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quf‘)““ 5,335} * '3‘='“f=‘i d) What test score would a student need to have a higher score than 90% ofﬂthcpopulation?
“‘x a I wit—(gnu —, Hg x“ GODL132}: .KW/ag'gf >1 .dri" e) What test score would a student need to have a higher score than 80%"6ftﬁe'p0pulation? ﬁx 3t} . X“._.._b_” \(3 6004 67.2 ‘ (>6 423 t“ \ ...
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 Spring '07
 Guggenberger
 Least Squares, Linear Regression, Normal Distribution, Regression Analysis, Standard Deviation, regression line

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