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Unformatted text preview: Fnstrueters:
Duratlen: Cemmeree ease  Camputer Augmented Business Etatlstiee Midterm Examlnatlen 1 rsian 1 ' Fall Term. 213411 T. Saltshury and GD. Weselewsky
2 hours Maxlmum Merits: 65
Ititleleher 13. 2001 Last Name: 553% Flrst Name: Seetien Number Student Number lnstmetlens: 1. This mtnatien has 15 pages and 5G quastlens ‘r'eu are respenslhle far
ensuring that year may at the paper is eempiate Brlng any diserepa ney ta the
attentian ef yam intrlgtlater. All questiens are to be answered an the aeeampanylng DMR sheet. Use at enty
the MeMaster Standard Calculatnr [Caste 1x991} is pennttted. Tables are an the last page. G. Mutﬂple Chaise  Prahlerns HIDEH} TOTAL maximum 3. Thls exam must he handed In slang wlth the GIMP. sheet. The exams and the
DMFt sheets 1will he aeﬂaded tagether. ﬂat: the DMR sheets wﬂl be marked. Please flll In the nude far your student number an the ﬂlh'lﬁ'. sheet Emmi.
cheek and deu hle cheek. Please read the DMR lnstmeﬁane an Page 2. mtlnued... 2011.3 Midterm blame
1. You are writing version 1 of this exam. Indicate this by answering a. for this
CL question. You MUST do this correctly. Discrepancies will be investigated as
possible attempts at academic dishonesty.
section A. TruelFalse {2  251
2. It Is assumed that a sample contains all measurements in which the researcher
is interested. Fr
3. As a population becomes large. it is usually better to obtain statistical Information
from the entire population. F
4. Ftatioecaled data are considered to have the highest level of measurement. T
5. Nominally scaled data are considered to have the weakest level of
measureo'ienl. T
b. The larger the number of observations in a numerical data setr the larger the
number of class intervals needed for a grouped frequency distribution. "T"
‘i'. The mean is a measure of central tendency. ‘T
El. The Session 1ii'Il‘Indow Is used to enter data into lvlin'rtab. F
9. If A and El cannot occur at the same time they are called mutually exclusive. "'T
10. Suppose there are three events A. B. and G with probabilities:
Pie]: = H.512]. PtEl‘l = bill]. FIG} = CLUE.
else. A and B are independent: A and C are mutually explosive:
Pie and C} = .El5.
Based on the above. El and care independent. F tiff5 n [1)? p {B} e 151(3)
11. The number of cars that go through the drive~in window at a local bani: each
hour is an example of a continuous random variable. F
12. In a Bernoulli trial there are two and only two possible outcomes. T
lb. The probability of success changes from tdal to trial in Bernoulli trials. F
14. The dishtbotion in which the mean and the variance are equal is the uniform distnibutlori. F, 3 continued... EDAE Midterm blame 15 The probability that a standard normal random variabler E. is below 1.95 is
cares. i3 i? is r ift ti) ~— “Tina—if 16. The probability.r that a standard normal random variable. I. is betwaen Lilli and
sooaunsrss. 1” Hialssia'rtﬁssE—Jtirie 1? The normal distribution approximation to the binomial works best when n is small. F 15. a numerical measure of a sample is sailed a sample parameter. 1: 19. As the sample size increases. the effect of an extreme 1.ralue on the sample
mean beoomes smaller. ’ﬁ' 2D. If the population distribution Is skewed. in most cases the sampling distribution of the mean can be approximated by lite normal dishibulion ifthe samples contain
at least 3i] observations. "T 21. As the size of the sample is increased. the standard deviation of the sampling distribution of the sample mean fora hemrallyI distributed population will stay the
same. F 22. Fer a particular sample from a ﬁnite population. the sample fraction was listed as
13.115. If the sample size was T". the population size was 14D. ‘T 23. The mean of the sampling distribution of the sample proportion is equal to the
proportion of the sampled population possessing the charactedstic of interest. T 24. The mean at ttte sampling dishibutlon of the difference between two sample
means is equal to the difference bahteen the means of the hen sampled populations. T 25. in Market Area A. Elite of the shoppers but.r Brand it toothpaste. In Marttat Area
B. 40% of the shoppers buyI Brand I. Consider the sampling distn‘botion of php;
based on aspirates of iii] and 12D shoppers drawn from Market Areas A and B.
respectively. The mean of the sampling dishibutlon is .3 F l/Mt’n'F'e 1 Ta _Trb i ‘L'rr‘Ur :‘l' It continued... EUAE Midterm Name Sectien B. MultlpIe lt'.':heice  Basics [26 49} MUTE: ‘3? Reund yeur answer to match numbers in chelces. lll'l.'l'i~en reading tables, dc net lnterpelate. Fer example, reund veur ncrmal
deviate 2.513 te 2.91 is match the avallable digits in the table. A distn' teaticn that chews the pﬂgﬂpf chservatiens falling within speciﬁed
class intErvals is called ‘— . statiatlcal lnterence a sample a relatlve frequency distributicn
a pcpulatleh a frequency distributien Health care issues are receiving much attenticn In bath academic and pclitical
arenas. A scciclcgist recentlyr conducted a survey:r cf citizens ever ﬁt] years at
age whcse net wcrth 1's ted high tc twenty:I fer Medicaid but whc have nc private
health insurance. The ages at 25 unlnsu red senicr citizens were as fellcws: $0 6162 53 61 55 EE 63 63 69 TD ?3?374?5 TE Hi B1 31 52 EE 3? 39 9E] 92 Calculate the mean age at the uninsured senior citizens to the nearest hundredth Ufayear' >“2_ evalut‘rtn #11
tilt.00 years ’15. T3110 years H.134 veers SLED veers none at the abcve 5 CDl'liil'lLle... EDAB Midterm Marne EB. 1il'iihich of the following ls MDT included as part of the cutout frcrn l'u'linitahs
DESGRIBE command?r a. mean
t}. median c. standard deviation 6: nmﬂe e. all of the above are included In the output. 29. If either event A or event El must occur. then events A and E! are said to he mI.rtIi.iall1.r exclusive.
statistically independent.
collectiver exhaustive.
None of the above. agave 3E}. The following is the probe hiiitir distribution of the number of cameras sold by a store In one day. a ﬂat 1 ~ F 1 o.1s citT
2 [1.20 H‘s"0
3 [1.25 ['1 5.”
4 sea J73
5 0.15 :i S'
E CLUE .30 EelE What ia the expected number of cameras sold per day? a. 31]
3.15
c. 11.25
d. DJET
e none of the above is continued... EDAE I'vtldterrn 31. NEME If n = 1b and n = DJ, then the mean of the binomial distribution la DIE.
1.45.
EDD.
14.29.
2.1ﬂ. IrvTl ' Wat—J" A oonlinuoua random variable to equally lilter to assume any value between 1
and Q. What is the probability that thla random variable will assume a value lzlortlleeenlianlﬂTl"?r i=ol £11 3’5 1:3
ﬁlm epilogue?) = up.
213 none of the above
Flnd P{o5<zco.o}. b.3530
I11 915
13.5515
0.3035
none of the above Qualﬁllf For some value of E. the orebabillty,r that a etandard normal variable is. below I la
oaoao. The value of I la “031 r 5» oﬂlo
3.31 T‘ A 1 ung ﬂ.31 = ﬂ iﬂHD 1.93 [1.51 T oontinued... sass Midterm 35. name A sample at sea subscribers tc a particular magazine is selected tram a
pcpulatlcn cf aces subscribers. lt‘I upcn examining the data1 it is determined
that nc subscriber had been selected in the sample mare than case, the sample cculd nct hays been randcm. the sample may have been selected witheut replacement er with replacement.
the sample had ta have been selected with replacement. the sample had tc have been selected withcut replacement Whlch cf the fctlcwing statements abeut the sampling distribu ticn cf the sample
mean ts incerrsct'? The sampilng distributierr is approximately nermal whenever the sample size is
sufﬁciently large [ﬂeaD}. The sampllng distributlen is generated by repeatedly tatting samples at size n
and cemputlng the sample means. The mean at the sampling distributlcn is ,c. The standard datdaticn cf the sampling distrtbuticn is a. All at the abeye statements are tme. Fteccrds at an autcmcbite insurance ccmpany shew that 10% at its pelicyhelders were lnyalyed 'In an accident during the past year A randem sample cf #00
palicyttclders is he be selected. The standard error at“ the sampling dlstributicn cf the sample pmpertien is _
Ti ‘—  It ﬁt " TD D ﬂﬂﬂﬂﬂﬁ (11H 5 A—(rjl 11 a
BEETS _ Tr 1— I . at .
{1135? ET: ’ “(7” 1H} g ncne cf the abcye E ccnttnued... sﬂea Midterm
33. Ne me Population A has a mean at ir'ﬁ and a standard dcvieticn pt 15. Pcpuleticn E has
a mean cf 1nd and a standard deviaticn pf 2t}. Ccnsider the sampling distripullcn
at s A — s E. cased ch samples cf size 1554 drawn from Pcpuleticn A and samples at
size dﬂ drawn frcm Fcpuleticn E. The variance cf the sampilng dishihuticn will be .25
.1 ,J 31.3? §——  Fad—+6151 Halvrlﬂl‘ier as iii—“s av.1 ma ' Ur are ' 1' 14 Fern.r percent at the people in Pcpulelicn A and Bullt. at these In Pcpulaticn El
drive a Emigmde autcmchile. Gcnsider the sampling distdhuticn cf pi — pB
based cn samples at size 115 and 125 drawn. respectively. ircm Pcpulaticns a.
and E. The variance cf the sampling distributlcn l5 Mi} Tﬂﬂui' WERE mﬂ=11§ emu—"'13
H.3ﬂ
c.0514 e r g _
lliﬂ 6 : L {it 1E). Jr Trish 1—1—53
ﬂﬂﬂEﬂ Pe'Fe mg m“
__ one + an
in? 115’ 5' centinued... Juan? gHsi'u ﬂE=IDD £31110 mashemﬂre sons MidtenTr Hams Section E. Multlple choice Problems Hi]  5D] MUTE: i}
ll] lit}. 3;
s. 41. eases eee®e Round your answer to match numbers in choices.
1.i'u'hen reading tahlesI do not lnterpoiate. For eitampler round our normal
devlate 2.913 to 2.51 to match the avallahle digits in the table. The numbers 1. 2. E are a population. The 1«variance of this population is:
.5 1+1+L, 2. [it—sitar 11—3. "“  l JR” —3' = 3 g :: —— 45T 315 ._ ‘Tt i4 '51
312 —'— 5.24 3 The prohahllily that house sales will increase in the next 6 months is estimated to
he D25. The probability that the interest rates on housing loans will go up in the
same period is estimated to be 034. The prohahllity that house sales or interest
rates will go Up during the next it months is estimated to he ELSE. The protestillltgi.r
that bath house sales and interest rates will increase during the next ii months is: gm Wei=15” tithes smug.3121
iii: mm = mm Pitt. ~ FittclE
Elm amt =t1fti’t'urvsﬂttn1‘) none of the above The number ofway's 4 ohgecta can he chosen from a set of T is: 3443 ’1'} _ Li— .5: as “r ’ titﬁst ﬁfisjﬁgfsi
21D 12D noneoftheahove It] continued EDAB Midterm Name 43. A t's'in'lplengluI has a new preleet under vva1.r anti selects ﬂve exeeutivea fer a transfer
trem their eunent jeba. a. repert had suggested that T5% at all exemtives in this
eernpanv weuld like this new ieb. What is the prebabﬁitv that exeettv three ef the ﬁve aeteeted Iii'tﬂ their new jeb'?
m 1 F Tl. ‘ ."l f
i a. 0.0204 b. [1.4219 . 3 CE? erase PM???) 1 311. 1.73 L131
ease? ‘  e. eases Let it be a hen'nailv distributed rendern variable with mean 100 and standard
deviatien 20. Find it such that: Fit tﬂixtx'FﬂJﬂ. "6 ﬁlij €110 FEIWEXEHUFPKDEZEHZE
. 12a =Fihé15,3'j:11e”f .3 El. T.H~=.iﬁil3+.l=_lall5—' bH‘LZagl
E 124 _tlxﬂgﬂhgslgeigb+‘slxlb 45. The en—llne aeeeas eernputer service industry.r is grewth at an extraerdiharv rate.
Current estimates suggest that enlv 200i. ef the hemebased eernputers have
aeeess te enltne sendees. Thls number is expected te grew quieth ever the next
ﬁve years. Suppese 25 needle with hemebased eemputers were randernlv and
independently sampled. Find the prebabilitv that fewer than half ef these
sampled eu rrentlv have eeeess te enline aerviees. Lee Iﬁi‘ﬂ mtg:
neat m. Eire35? if Hm I]. e. uses 1 , a. bass. fie5T : 13:4: 10 e 0.000 m 3 ii seas Midterm
46. Name The amount of time it takes to complete an examination has a skewedleft
distilloutioh with a mean of 55 minutes and a standard deyiation of 3 minutes. If
64 students were randomly sampled. ﬁnd the probability that the sample mean of
the sampled students exoeeds 1'1 minutes. 1 E— : :_ 1:: t " “
Approximatelyt] “M L3 g E m" E f]; 3031 5 >5 so mate
oases r 1/“ :. t3; if; _ ._ 2 _r ]
oars: "_ s at?» m
Approximately‘l 'F [x “tr—[1‘3 : ‘P ('1 Hr. 'Ttlaf : F. a E :13) Reoords of an automobile insurance company shoii'ir that 10% of its policyholders
were inyoiyed in an aooident during the past year. A random sample of son
policyholders Is to be selected. Suppose the oompany has a total of ssoo polioy
holders. The probability that the sample proportion of polioy holders inyolyed tn anaooldentlslsssthanﬂ‘ittis . szv'i “:1'Jt'BD ﬁll—"2.3110
ﬂ—n—nm :EILhLDE—T JILLML ossts ﬁt ' 150“
0.3er m L‘rrF \tﬂt} s at 9W H a 5'1 J; View
t}.i]?35 r _ : 3
t ‘tt‘ — h 13:1 a
ﬂaws Egg“ #lgﬂ: 3,1_ Lesa. statsm 3373 sea: 3} MW'
ﬂﬂﬁﬂﬁ _ 5 N_m _ F3 1‘ Hm, : ms
EIF‘ELT'J Q" " ’i Mai '— oo s‘tﬁ‘t ‘
Fteoords of an aUtornohiIe insurgnoe oomp/rﬁy showt t 1 “it: of Its po ioy lders
were involved in an aooioent during the past year. A random sample of AIDE!
polioyholders Is to be selected. The probability that the sample proportion of polioy holders inyolyed in an aooident is between 9 and 10% inolu she is   arses W11" “‘1': UCDD 2M Mldterm 49. assets 5!]. Name Researchers believe that the amou nt of time in hours per month spent watching
television by children ts an approximately normally distributed yarleble in each of two geographic areas. The population means and standard deuletitms are as follows: _ E .r't'L “— " i — so
Standard m '4 1 E inf “r (iXqu H E) Area Mean dayiation melt/17mm}? W
e tt'o—Fpa so=sﬂ ﬂay—“'13 :ﬂe_ 3—1:!ng
A 190 2;“ 4t] :s'ﬂ 6, h {1 ET “mi L
' _E " H + L t. — :lr —
“it ‘3 on an: ago i Suppose that independent random samples of she a; = 4i] and on = ED are drawn
from Areas A and B respectively. What is the probability that the difference
between sample meansI s y  s a. will be greater than at} hou rs? _.— 1 3 —
osm iﬂiLKﬂXQ 5312*] : Pﬁl 3‘ w 13%}
cases
c.3413 : Ptlhih
D3413 1 _
p.153? ‘5' 3m?“ Researchers with an oil company belieye that the proportion of its credit card
holders who make at least one outofstate purchase during a year is the same {DAD} in two sections of the country. it they are correct. what is the probability
that a random sample of 100 customers trom Section A and a random sample of 125oustonterstromSectionEwtllyieldsdil‘lienttnoeditypa.5reetertl1anillslil'iI
iiﬁ sTFEE‘iF my =iDD mﬂ=llh asset as on  new i ~ 333i: new {new} a toasting ’3 3': “ Wigs mﬂl‘ﬁ—E: illjilitx'i": o5 item “uni:75 h _ itaitrmi if mm
_. TE~TE ' liq—Ht“?! TE, Sign—iced "#13" ET JV.—
‘nmh ‘ 1st: _
_ too + _:"tﬁ# HJLJEI?
PH 13 continued...
1. 1:1(2 2: 1%“ a '19 (2 bltFo) b5t‘t35'7 ZQAB Fa rmula Sheet
Pawn} = pm} + pm} _ mm} Pmnm = I'm In) Pm} = Fall A: Pm} Rule I: :11 111 Run: 2: n‘ Hui: 3: nIIILrIr}! Rule. 4": nlﬂrlinrjlj
1: xiv{11w}! P{x}= Iliﬂr]! nil11:)”; E{x}=n1t; VARix]=m1:(1Tt} Ew}=n: UP: 1:!1113 ﬂ
ﬁx1= w—i— where stsh; I1= ﬂ :1: h“!
2 m
_ EX. Etaﬂ
I“ h: Si: ['1
n 111
1': 2 1 1
 5 l3'1 5: 15' g
u I: _..._ u.._  ._+_ r 3  I: _" __
I 4:3 “I m a: ’"’= n: * u: ﬁlaﬂfﬂrstddw. = E
I 1' N—l I. I. I ...
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This note was uploaded on 12/21/2010 for the course STATS 2QA3 taught by Professor Buchanan during the Spring '10 term at McMaster University.
 Spring '10
 Buchanan

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