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Unformatted text preview: r“ Paul M. Sommers I; .I ‘ I Fall, 2007
tau; ;
(.rJL—— Economics 210 5
ECONOMIC STATISTICS
Exam #1
HONOR CODE (“1 have neither given nor received
unauthorized aid on this exam. ”)2 Signature Please print your name You have up to two and ai‘half hours to complete this 100 point exam. Be brief and to the point
since only the main point(s) asked for in each question will aid your grade while a display of
ignorance can count against you One point (up to a maximum of three points) will be deducted '
(from any extra credit points you may have accumulated) for each miSSpelled word in either the
“Honor Code” (which I ask you to write out) or in your answer to a question in which the same
word is used (and spelled correctly)._ Please do all questions and show your work. (No credit
without an explanation. Correct answers without any Work will be penalized.) Good luck, happy
landing, and remember that half of all Americans can t do math. .and the other twothirds
simply don’t care. AND LET‘S NOT FORGET 
THE NEAR GRTAINTY
THAT YOUR FORMUlAE
ARE POINTING TO THE
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MY $PREADSHEET. YOU
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"111 canmﬂcou Adam.lnrJDMJy Umlne. www.mlbannom would!anch 1 1. _ (15 points) The entrance fees for adults to 14 theme parks and attractions in Orlando,
Florida are listed in the following table (from highest to lowest, with two missing
observations). ' ' Theme Park/Attraction , Entrance Fee ($)
(xi) .._..... ' . a. t a 2"“ n.
Blue Water Hot Air Balloons 185.00 2:
Universal Islands of Adventure ' 63.00 ' 7526’ Sq 14'
Universal Studios 63.00 4?
Sea World Adventure _ _ 61.95 a» 53:04‘
Disney Animal Kingdom _ . 56.70 . , _
Disney EPCOT Center 56.70 b [g 1046501! a [ﬂag
Disney Magic Kingdom 56.70 ‘ _ +5»
Disney MGM Studios  56.70 behalwa W 7 Disneerest _ 35:00 and gﬁ§£kﬁéﬁéyg 3.
73‘5éﬂo ' Disney Pleasure Island ” 20.95 Universal City Walk . _ 11.95 ‘ 0 e 12: 5;
Disney Wide World of Sports Complex _ 9.00 @l M d ' lb 14 14 d ‘ g Pg) (”a deg?“
n =14 in x 728.59 Ex} = 621293 W53. W 15246411
I ‘ ' /E [at Wren W (3) a. What is the mean entrance fee (to the nearestpenny) for all 14 theme parks MMM
(even though I have excluded the entrance fees fortwo of the fourteen, namely,'Gatorland and Holy Land Experience)?
(2) b. What is the median entrance fee for all .14 theme parks? (1) c. What is the mode? (2) d. lsthe entrance—fee distribution symmetric about the mean? 01‘, is it skewed
to the'leﬁ or to the right? Why? . 7 ‘ ' (4) e. What is the sample standard deviation, 5? {Note: Your answer should be , '
expressed in “dollars”, not “dollars squared”.} ‘ (3) fl ' . Use these (fourteen) values to ﬁnd the zscore for Dollywooa’ (in Pigeon
Forge, Tennessee) where admission is $40 a person. 2. (4) (6)
(2) (3) 0% éam‘" 3: {[375 (7/th K #ﬂﬂ‘?
M31937  a glam/mt Java/79w 4% mg ml q
.3 (15 points) Suppose that ULT RAM/1R will provide home heating oil this winter to
. 1000 local residents in the following (probuy) amounts. _ Heating oil Number of
(gallons) customers
500 " ' 275
1000 ' 350
1500 ' 200‘
2000 175 a. Find the mean (number of gallons of heating oil) for these grouped data.
{Note: Since your answer to part (a) will be needed to answer part (1)),
please doublecheck your calculations} b. Compute the standard deviation. c. If home heating oil is $2.79 per gallon (the prebuy priCe),on average how
much money (to the nearest dollar) will ULTRAMAIR collect on each pre—buy contract? d. What is the standard deviation of thecost of the 1000 (probuy) contracts? (0730 #3755“ 2'75“ +1.,+ *(Zowﬂ/ZZEB‘? xi’fc‘i‘
was "‘1' 5’ £245 aims; *“x 3. (10 points) The following crosstabulation of smokers by sex is based on the
responses of the 67 students who showed up on the ﬁrst day of classes. If
“Smoke?” = 0, the respondent is not a smoker; otherwise, if “Smoke?” = l,
the respondent is a smoker. If “Sex” = 0, the respondent is male; otherwise, if “Sex” = l, the respondent is female. LetlA = {smoker} and B = {female}. Tabulated statistics: Smoke?, Sex Rows: Smoke? Columns: Sex 0 1 All 0 38 20 58
65.52 34.48 100.00
84.44 90.91 86.57
56.72 29.85 86.57 1 7 2 9
77.73 22.22 100.00
15 56 9.09 1343
10.45 2.99 13.43
All 45 22 67' _67.16 32.84 100.00
100.00 100.00 100.00
67.16 32.84 100.00 'Cell Contents: Count
% of Row % of Column_
% of Total Please use the cross tabulation to ﬁnd the following probabilities. (2) a. I‘p(A) ‘ 7 . 4 (It: ”3 ﬁIfge/Z.4B%& ,
.. i has be; (22.4%:
(2) c. p(AlB) ' ,gég/ [55a ﬁ/m (=5 eff/04%:
gig/4; % 5. WM: [Mng 3%r( 5572743 (2) d.. pdélA) . a}
' _(2) ex 005)} J 4. (15 points) The US. Census Bureau reports a'decline in the percentage of mothers
' with infant children in the workforce. The following table gives a breakdown of the
marital status of the 3.934 million mothers with infant children in the year 2000. (The
' numbers in the table are reported in thousands.) Censider the following events:
A = {mom with infant works} and B = {mom with infant is married and living with hitsband}.
 Working ‘ Not werking
Married and living with husband I . 1385 , I .1175
All other arrangements 786  588 Source: US. Census Bureau, American Demographics, February 2002. (I) a. Findp(A)_  4. $.(Ag‘ﬁ2ﬂ7y34g4 “M552 (1) b. ' Findp(B). [9’ féggu {BER/3454 “,éB’I (2) c. Which is larger: p(BA) or p(AB)? What is the probability in each case?
(2) d. Which is larger: {1(ng ) or p(AI E )? What is the probability in each case? (4) e. What fraction of all working moms with infants are neither married norliving
with their husband? Simply write this probability in terms of A (or A ) and
B (or B) using a vertical line forthe conditional symbol, I . _ (2) f. What is the probability described in part (c)? g. Are A and B independent events? Why or why not? ' g t Mayan a 25%,}; (agar;
( [A  {4&5 [Mtg 2: 133%55; (1.53415 5. (15 points) .Middlebrewery, a small brewery here in town, has two bottling machines.
Machine A produces 75 percent of the. bottles and machine B produces 25 percent.
One out of every 20 bottles ﬁlled by machine A is rejected for some reason, while one out of every 30 bottles from machine B is rejected. (5) a‘ What proportion of all bottles is rejected? (5) b. What is the probabilitythat a randomly selected bottle comes from machine A,
given that it is accepted (that is, not rejected)? (5) c. What is the probability that a randomly selected bottle comes from machine B, given that it is rejected? Lef T111, 5 g 4” We 34mg: 4”” MACAIE 4f . Please show your work. _ I451 ' g  We (£09199 {ﬁrm madhlhé ﬁg 7 ,4; w'Eédf/eré " f 4. }Kr&=}(a4+#14&:f%%%rg 6. (15 points) The mail order catalog department for Bearly Right considers three possible
foul ups in ﬁlling an order: . The bear [5 lost in transit
B: The bear is damaged in transit
C: The wrong bear is sent Assume that events A and B are mutually exclusive and that event C is independent of
both A and B. The individual prob“bear”bilities are p(A) = .07, p(B) == .04, and
p(C) = .33. That’s right, p(C) = 33 percent! .7 (4) a. Find the probability that at least one of these foulups occurs for a randomly chosen order. Please report your answer here and elsewhere in this problem to '
four decimal places. (2) b. Is your answer to part (a) given by:‘ ‘—l —p( E )p( E )p( E)“ ? Why or why not? , Mk? (
(2) 0. Describe' In words the event (B )( C ). What (If any) kind of foul up is this? ééﬁ‘dga / £154; :
 7” p2 I agar 22.; . (3) d. Find the probability of ( B )( C ). , igZEdB:
' 515 l (4) e. Find the value (again, to four decimal places) of p[Al( E )( E )].  H atc‘E (at453 E
a EZAECE [If/E lifting “'4 ._ re? 44.04 ha?» * 597E653§
 ”604E 535E
“ 4037 (/hlEnreXE/H/EC/ as (532 45/2? f _ _
5E; Egmée 44/ hitter Kevin’s >fm 4 E Ami d “Wiffﬁiﬁi/ a. ﬁns/97+ [53:55;
j g 9(ng I] EL’EE
_ fit/(erg (3)
(3) (3)
. (3) (3) b p(CIA) , jg:
.c. p(A[E) _  .
d p(BlAC) 6} p(ABl5 )1. (15 points) Two hundred (200) borrowers currently hold home mortgages with a local
bank. Information has been collected on their monthly income (C1), the price of their
home (C2), and. the number of years of seniority they have on their Currentjob (C3)“
The column name for C1 is ‘INCOME’; the column name for C2 is ‘PRICE’; and the
column name for C3 is ‘SENIORITY’. Now suppose we deﬁne three events: A: Borrower has monthly income exceeding $5500 _
B: BorroWer has purchased a home whose price exceeds $250000 C: Borrower hasjob seniority of 15 years or more Use the computer printout on the next page to answer the following questions. (Recall
that the “sum” command adds up the numbers in eachcolumn.) In this problem, please report the probabilities to th edecimal places. _ a. pus) gm!— jihu'ja’ le/maﬁée 12m @Mm
; J 4' 
Qty run a tee ah ' Results for: BANKJOB‘LMTW. 'MTB > Let C11 =
MTB > Let C12 =
MTB > Let C13 =
MTB > Let C14 =
MTB > Let 015 =
MTB > Let C16 =
MTB > Let C17=
MTB > sum C11
Sum of C11 Sum of C11 = 116 MTB > sum c12 Sum of C12
Suﬁ of C12 = 33 MTB > sum C13 Sum of C13
Sum of C13 = MTB > sum'c14 . Sum of C14
Sum of C14 = 32  MTB > sum C15 Sum of C15
Sum of C15 = 23
MTB > Sum (:16 Sum of C16
Sum of C16 = 13 MTB > sum C17 Sum of C17 Sum of C17 = 13 24' 'INCOME'
'PRICE' 'SENIORITY' > 5500
> 250000
>= 15 'INCOME' > 5500 And 'PRICE' 5 250000 'INCOME'
'PRICE'
'INCOME' > 5500 And
2 250000 And
> 5500 And 'SENIORITY' >2 15 .
'SENIORITY' >= 15
'PRICE' > 250000 And 'SENIORITY' > 15 ...
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