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Unformatted text preview: Economics 41 UCLA Fall 2008 NAME (Print) by A 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 crasers 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 True/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 (e.g., UCLA ID, driver’s license, or something similar).  You may leave when ﬁnished. Turn in both the exarn and your scantron. Do not disrupt those still taking the exam. I. Circle either T for True or F for False (2 points each, 30 total). IQr F A sample correlation coefficient may be calculated between two quantitative variables, but NOT two
qua itative (= categorical) variables. 2) T or®Time series data on one variable can NOT be represented in a histogram. 3) T [email protected] If the sample correlation coefficient between X and Y = 1, then the slope of an estimated regression line
of Y on for the same data sets must also = 1. 4)®)I’ F The U.S. national “federal" government budget deficit is a flow variable. [ i
. IQ t?
5) T or®For all boxplots‘ the “whiskers" extend to the furthest observations which are less than 1.5 quaﬂiles below
the first quartile, or 1.5 (3.96“? above the third quartile.
0:3 66)“ F For a histogram with relative frequency on vertical axis, one can not determine the number of observations 7) T or®The slope estimate for an ordinary least squares regression is “resistant" to outliers, but not the sample
correlation coefficient MW 8) T or®0iily data from a population that is normally distributed can be “standardized. ” 9) T or®For any “reverse regression” the estimated slope: b" is the reciprocal of the estimated slope of the forward regression: b1 l x—ll
, . . . . 1 ‘" a . .
10) T or®Since the formula for the probability of a normal distribution = ———e 2[ ] the normal probability JVZK density curve is highCSt when (x—tt) is largest. 11) T or® For three observations: 3, 4, and S, the sample standard deviation = .8165
. . . . ’3}. 12) r F 5. IS a statistic, while ‘. is a parameter. 13)®or F An observation may be an outlier in univarate analysis, but not bivariate. 14) T or An outlier must be an inﬂuential observation. 15) T or®lf the sample correlation coefficient = 1, then we can be confident that changes in X cause changes in Y. yell/i Omani 69W? raunrlmg of 2  Mid I . BRIEFLY, clearly and correctly ansvver 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 of4 minutes. If students are 'v ish, ﬁnd the proportion who will complete the exam. V l 2.
2) The scores on a university examination are normally distributed with a mean of 50 and a standard deviation of 10. If the tap 16 % ofsrudents earn A's, what is the lowest mark that a student can have and still earn an A? .Btn. = “7? a" 936% : “To” x: 50+ 5: 39¢
 I ' 5“: .399 e.
X: ro'l 9‘1”; '67 _F _._ Ci
‘ " etﬂlhﬂr 0k .. _——~*’ 3 3) An economics department with 40 allmale faculty which hires two per year, has two retirements per vear (each after a
20year career) wants/tedravéZS‘W female faculty. What will. be the gender of the ﬂow ofnew hires ifthis goal Is to be metinIOyears? IF‘EMIE’ .l lmlP Per VW.
so. a: remit P’DW m_hw_ _J__ ..___._.._ _ _ .,.._ ‘ .. 3
4) For an ordinary leaxscluares regres ' ' e, if x = X , what is the predicted height of the regression line for this
x?
Y )(r )L 3 S) The average earnings of individuals with an undergraduate degree in economics is higher than for individuals with an
undergraduate degree in business administration. Brieﬂy give three reasons provided in class. —€ron peel}! psi real wade“)
_ {From pnptlot underage?! m‘[email protected] 8H9 itself/ism lush FlanrLtl“ fl HOV luajiré go in g‘ml retrial“) 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 mo of “service" (experience)? Regression Statistics H we (8+ Adrian) LOS 0.40 Nev/4 7) The diagram below show the number ofjumps for each of 24 student. The variable we consider is number of
w!“ jumps.
at x L6ltklﬂll9
x x l
x x x ‘
x x x x x x x \
x x x x x‘ x x x x/ l m t try n ﬁt": '41 en Etc: =0:‘: I
Number 0! Successfullsumps
What IS the median ;a.nd the mode:
[Jrta] ll a W 8) In the f ula from the text and class: ——e ,what is the numerical value, 0 (three signiﬁcant digits)? 0J5:— 9) What jsminimized in ﬁtting an ordinary least squares regression line? Use summation notation, not words. \(Eeaz W {(77% Dr EGWbD—hMB—L 0W2; 10) A sample 0.40rkers 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 propor______t___r'on of black workers 1n the sample?
II ., ‘2 6’3
(5’0 COURT I] I! white black asian other HI. Clearly, concisely, and completely answer the following problems. Show your work. (10 points each, 40 total).
a f f 1) Let X hourly wage feta sample of 9 workers. The values of X are: 30 34 55 15, 20 18.2S,18 2_8_ a) Make a stemplot to the tar right (do not “Split stems ) and a histogram with classes: .x ' “"x\ . below, as done in Ihﬁjﬁlxt (with lower but not upper values included) x Era.
_""
.200 ’9 Pa .3, If!
m__.,.. b) What is the (sample) Mean? 0) What is the First Quanile, Q.?
(use text‘s method to find Q. and d) What is the Interquartile Range (IQ KoxlA I 2) Consider the following data on X and Y: 21) Find val *‘u' i) D:
1] ii) it»)? i=1 iii) (in)2 72“ W ———~
,=. 5 (u. LIM 2c “(56‘ nﬂ (1027) b) Use either your calculator or the rmulas on the last page to ﬁnd:
 l 5‘ 2
b1 i. t i '3 A  I‘ g 6 i) sample correlation coefﬁcient  5 li
a 1
ii) slope of the animated OLS regression Ii with x the independent variable iii) intercept of the estimated OLS regression line with x the independ 1 variabl’:
'5 b to . \t lax '~ ii — .. =2 75+ 17011: ll‘l'; w bmuw..." W
3i Consrder Excel output to the right. W Regression Statistics Y = overseas returns (in %) and X = US. returns (in 9:3). 31:13:? 33338
_ _ g .
X = 3 and Y= S s = 4 and sY = 6 Coefﬁcients
V: '2 '5 l. q x Intercept 2.30
a) For the forward regression Y = b +b X what is the predicted US 0.90
value for overseas returns if 3 _ '5 hit = 6 12’ q
. '" 1
 .. 9  ‘ i ’2 7 ' ’ ._
U_S. returns are. 5 percent. US. returns are 11 DEWW i ' l5?)  '3 “,IICSS
mouse A _ _ _ ': i
 what Is the pred1cted value for US. ret ‘ .  [ﬂierI} he .W regression X = 1 Overseas lrenrtmsB are: 5 percent. Overseas returns are 11 percent ”3‘3 ’2' ”.4613 or a particular population, assume test scores 0 ow a no 1 I1 11 ton w1 popu atlon mean = , an
population standard deviation = 80
'20 D
a) The standardized z—score corresponding to a. raw score X = 800 = 325 7' ,1
b) What proportion of this population sowed below 800? qq 3 2 '1. a so too A,
c) What proportion of this p0pulation scored between 650 and 800 .2 9 U c . i 2 g A: . E 3
.‘mav .73” =,2€8 ' d) What test score would a student need to have a higher score than 90° .' o Iuiation? 18 r. ‘KebOU “4 :
I. ,8” x 601mm: 2. e) What test score would a student need to have a higher score than 80° 6 population? N L ‘ X'690 \{3 00467.}
thjr E 6 1’ ...
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 Fall '07
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