Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OOT

Question 1: Multiple choice: circle the best answer to each question:

(1)[2 points] A reader of the Indianapolis Star wrote in to express doubt that a poll based on

a random sample of 600 voters is sufficient to estimate the proportion of. 2.5 million voters

favouring a certain candidate in an upcoming election. This reader's point is

/4.((a)')not valid: variability of sample statistics doesn't depend on population size as long asV the population is at least 100 times larger than the sample.

(b) valid: a sample of size 600 is much too small.

(c) not valid: all election polls use this sample size.

(d) valid: samples of size less than 1000 are often yield biased results.

(e) not valid: samples of size at least 200 are always sufficient.

(2)12 points] A study was conducted starting January L 2007 to examine two treatments used for

prostate cancer. The study used medical records of prostate cancer sufferers over the past

ten years. The study found that patients treated with surgery tended to outlive those treated

with a non-surgical procedure. This study is

(a) an experiment

(b) a completely randomized design.

f(}ut observational study.\-7(d) a matched pair design.

(e) a block design.

(3) [2 points] The attached table of random digits beginning at line 125 is used to select a sample

of size five from a population of size 140. Individuals are labeled 000,001,.... The label of

the second person selected is

(a) 001

(b) 002

(c) I2I

(d) 11e(t}rors\-:/

(4)12 points] A poll based on a survey 1396 randomly selected drivers concluded that 63% speed

at least some of the time. The poll has a margin of error of approximately 2.5 percentage

points nineteen times out of twenty. The margin of error divided by the standard deviation

of the sampling distribution is approximately

(u) 1

(rilrz\-7(c) 2.5

(d) rel2o(e) cannot be determined

p . 2 o f 1 3

Math 161 Sec FO7N01 & F07N02 - Practice Final ExamDec 10 2OOT

(5) [2 points] Comparing treatments to control the effects of lurking variables is known as:

(a) Simple Random Samples

f(U) nanaomized Comparat ive Experiments\:-Z

(c) Statistical Significance

(d) Comparing matched groupings

(e) The Placebo effect.

(6) [2 points] The best method for testing causation would be:

(a) Sample Surveys

(b) Observational Studiesn -(9 llxPerimentation

(d) Census

(e) Polling

(7)[2 points] Repeating a measurement five times and taking the average value

(a) reduces bias and random error

(b) reduces bias only,r^\ I((c))reduces random error only

(d) reduces neither bias nor random error

(e) none of the above

(8)[2 points] Based on data from 1998 to 2000, Columbia has the highest homicide rate in theworld with approximately 61.8 homicides per year per 100,000 residents. If the population ofColumbia is approximately 41, 008,227, approximately how many deaths annually are due tomurder'/

(a) 10,000

(b ) 15 ,000

(c) 20,000

fralzs. ooo\-7(e) 30,000

(9)[2 points] Temperatures of four fish market freezers were taken and found to be 3.3,3.7,4.7and 2.9 degrees Celsius. What is f - s?

(a) 2.0

(b) -2.0

(c) 0.75

@ r o(e) -3.0

p . 3 o f 1 3

Math 161 Sec FO7NOl & FO7NO2 - Ptactice Final Exam

Dec 10 2OOT

(10)[2 points]

r l 4 5With reference to the sample represented in the following stemplot

3 32 l r 23

8 9

A ,@/ tt e mean is 26.875 and the median ts 22'5

(b) the first quartile is 21

(c) the median is 22

(d) the maximum is 88.5

(e) none of the above

(11)[2 points] The median of a distribution is larger than the mean when

(a) the distribution is skewed to the right'z,4(U)'lttr" distribution is skewed to the left.

(c) the distribution is symmetric.

(d) the distribution is represented using a stemplot'

(e) the distribution is normal.

(12)12 points] The following boxplot summarizes data for populations .4 and B of equal size:

(a) the median of ,4 is less than the median of B'

(b) the median of A is less than the first quartile of B'

(c) The corresponding distributions are right skewed'

(d) (u) and (b) only.

@t"), (b) and (c)'

p . 4 o f 1 3

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OOT

(13)[2 points] Referring to the boxplot in (12),

(a) the standard deviation of ,4 is less than that of B.

((i,)ttr" standard deviation of ,4 is greater than that of B.v(c) the standard deviation of A is about the same as that of B.

(d) the standard deviations are the same since the third quartiles are equal.

(e) none of the above.

(L4)12 points] In a normal distribution, the percentage of values that fall between one and two

standard deviations from the mean is approximately

(a) e5%(b) es.7%(c) 68%

(a\zzn\-7

@) 5a%

(15)[2 points] A large class has test scores which are normally distributed with a standard devi-

ation of 5.5. The percentage of the class scoring at least one and a half standard deviations

above the mean is approximately,,^((a\\ 7%\-7(b) e3%

@) a3%(d) 44%

(e) 68%

(16) [2 points] The correlation for two variables is calculated to be r : 0.72. Which of the followingvalues of r indicates a stronger linear relationship?

(u)

(b)

( . )

(d )

I .2

0.68

0-0.72

-0.83

p . 5 o f 1 3

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OO7

(LT)12 points] Two researchers examine the same data set summarizing the trunk circumference(r, in metres) and location above sea level (A,rn metres) of 50 spruce trees. Both researcherscalculate the correlation, but the second researcher converts all measurements of circumferenceto centimetres first, and he instead uses r for location and E for circumference. If 11 and 12are the correlations found by the first and second researchers, respectively, then

(u) "t : l l rz

(b ) r t : 700 l r z

(c ) 10011 :1 ,,/Av))": "

(e) 10011 : I lrz

(18) [2 points] Let r represent the height of male students at Malaspina, and assume the distribu-tion of these heights is approximately normal with a certain mean pt and standard deviationo. A student calculates a z-score (or standard score) of z1 - 2 corresponding to a certainvalue of e, but then realizes the tr; and o he used were incorrect; the correct values of each arehalf as large. He calculates a second z-score .z2 using the correct values for mean and standarddeviation. How will z1 and 22 comparc?

(a) a will be larger than 22.

(6\r, will be smaller than 22.\v(") ,, will be the same ds 22.

(d) Because of the error z is no longer normal.

(e) none of the above.

(19)[2 points] In the distribution below

(a) the median is ,4 and the mean is B.

diltne median is B and the mean is C.\/

(c) the median is C and the mean is A.

(d) the median is C and the mean is B.

(e) the median is B and the mean is A.

p . 6 o f 1 3

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OO7

(2O)[2 points] In the scatterplot below

(a) r :0 .1 and the regress ion l ine is gr : -0 .5r * 1 .

(b) r : -0 .1 and the regress ion l ine is E:0.5r * 1 .

(ot : 0.8 and the regression l ine is a :0,75r + 0.5.\/(d) r : 0.8 and the regression line is g : 0.75r - 0.5.

(e) r : 1.0 and the regression line rs E : a.

p . 7 o f 1 3

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OOT

Question 2: A grocery store selling tomatoes must keep the inventory carefully balanced: too

large an inventory results in tomatoes rotting in the storeroom or while out on display, while too

small an inventory presents the risk of running out and hence losing customers. Reliable sales data

shows that on average 207 kilograms of tomatoes are sold each week, while the standard deviation

from this mean is 17 kilograms per week. Assume that the number of kilograms of tomatoes sold

each week is normallv distributed, and tomatoes are delivered to the store once per week.

(")[Z points] The middle 99.7% of weekly demand values fall between what two extremes?

Round to one decimal. You may use the "quick method" here if you like.

17.+ 7o /t alt va-h'ret +-!tL 6^7ifl-'r^ 3 st^*'fu('U - J ^ . * ' a ^ ^ - � - c . r ^

otev,ori *1S I .h*.^,.,*kr t ' t1- t '*o efEr?teS 4-'

Lo+ - 3 (t+) = F-i rb -bg ) -^tI/> (/)

20+ + 3 0T) - 2fg r<9 '

(b) t4 points] How many kilograms of tomatoes should the grocer stock at the beginning of

each week to ensure that demand is met 50 out of 52 weeks per year? Round to the nearest

kilogram.

2 = o " 1 6 l Y i 1 G , l Y ? " o + { ' r € e K f 'fL a

oav-<s t lv .d i ,g to a6 ' r t P€4c t t " t \ l ( ; s L - l -E' t o

bz +^e ,'"1* R'J s t'rc lc \euet ' Tta''-

Y - 2 : + , s o X - L o + + r ' 8 ( l + ) t @

l - 8L - 5

Le-t X

l " ( = X - 2 0 +t +

(c) [

points] Suppose the grocer has a long standing weekly order for 224 kilograms per week,

but he decides to increase his weekly order to 24I to ensure that demand will be met for a

greater percentage of weeks. For how many additional weeks per year will demand now be

met? Round to one decimal.

@ ? F'* D4 A"Jt T=

F w 2 1 1 - % t L = Z'11 - )o+ =t +

ro? lL+

n"n ?onc**7c- r+f '<J€**eJ bU

q+ ,7 }3 - vq , l 3

= l j . C ? o

? "-p(d^+Pr^"(v'>1-LK5 f*W

r J

'n' \ et'^*J arill b{- " e* +.. (o,t3 6 ) Cse) J

p . 8 o f 1 3

Math 161 Sec F07N01 & F07NO2 - Practice Final ExamDec 10 2OO7

Question 3: A game consists of spinning the two wheels shown, first Wheel 1 (divided into threeareas, the first twice the size of each of the other two), and second Wheel 2 (divided into threeequally spaced areas.) In a single play of this game you receive an amount of money equal to thetotal of the numbers shown on the two wheels. For example, if you spin a 1 on Wheel 1 and a 0 onWhee l 2 thenyourece ive 1+0 :1do l l a r . Anega t i ve to ta lmeansyouhave topay . Fo rexamp le ,a total of -2 mean you must pay $2.

(") [g points] What is the probability of receiving less than $2 (including having to pay) in asingle play of this game?

{ 2 i: tt r vnzq Kin '.'t^.wr ?%ot fa|t* l*? {'l€"-^ a- I et'"'-

t^rheel t t a I o* u.tv.eel L ,

" ' o ? ( f " S 5 * r , a - ^ z ) = l - P ( t t r = z )= l - P ( l 6 n . . s ^ l t . r e a l= | - G ) ( * ) = - t I ' o , s 3

(b) [4 points] What is the probability of of getting a total of. zero?

( L ) ( f ) = *

What is the total of the expected outcomes of each of the wheels?

eXQe ,te"l o**cau-,e = e t) ( t ) * {o)(L1) * ( ' )

Ou*c.a,,n€S it ? *O : IA

| ) P( | crr. -hec lZ ) !,^&'g'^r1"^,

^itJoi"t e,,p.*ts tBn.o-l< <v4

wu.ne I /------- l

L l

I

ev€.^,f "+oto,( Xjno" irth)

, ' lueel L ?-ot* t t ' ' t . i+:

| ( t . . { ) ( t ) : * -o ( t ) ( j ) = f r-l

+ z I' i-u- 3

(c) [3 points]

ssV..e-el | :

; V e e \ a t

oo o +?rt"t

exper*.J odq*'e

{ fte *,

P e *<rl

= (-r) ( f ) t ro ) (* ) t ' t t )

(+)( * )

.tI

= o

wheel 1 whee l2

7&,U,(s^

p . 9 o f 1 3

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OO7

Question 4:

(")[f points] Of a random sample of" 1764 seniors, 1135 felt that the current level of fullyfunded healthcare provided by the government was adequate, while 7l% of them felt thatmore support was needed to allow seniors to stay in their own homes for as long as possible.

Give a 99.9% confidence interval for the percentage of seniors who feel that healthcare levelsare adequate. Round to one decimal.

n - 116{

f i = l t35-tHrq

2* = 3 ,Lo1

i 3 z Y

e . t r 9 3 1 ! ? . L A o , " , { 3 q t - o , 6 q 3 t l

r +bq

o o . 6 L t 3 . t ! O . 0 3 {

(b) [5 points] A 90% confidence interval for the mean lifetime of a certain brand of lightbulb

was found to be 973 hours to 989 hours. The confidence interval was based on the samplemean and standard deviation of a sample of 784 randomly selected lightbulbs. What was thesample standard deviation? Round to the nearest hour.

71 : +81

a a

- l

173 I 1n{y - q 1 + 3 - = 1 t l

L

Xr+ z ' 181

+ \ - 6 q = q n

.o. v

q 8 lJv-

J?8LI

t 3 + h , " Jg,= (u5ryr)mq:p. 10 of 13

Math 161 Sec F07N01 & F07N02 'Practice Final ExamDec 10 2OOT

euestion 5 [10 points]: In its 2006 annual report, BC Hydro states that 85% of customers give

them a ranking of at least 7 on a 10 point scale of customer satisfaction. Suppose we conduct our

own test and find that 40 of. I75 randomly selected BC Hydro customers give a satisfaction rating

of.6lL0 or less. Is this result sufficient to conclude that the proportion of BC Hydro customers

satisfied at the T lI0 (or better) level is less than what is claimed in the annual report? Test at

a 0.04 level of significance. Clearly state the parameter you are testing as well as the null and

alternative hypothesis. Clearly state your conclusion'

L et D = p rW ortr ar. /t C,-<sfov'., +,rS 5b.z1's $-'"rf -f +Te| ' - t o

Zo (/\r bcn"* le,so(,

\ \ , . ' ? = o '8(

H ^ :? .

o " 8 t

fi I I S,ayf

*rt+L

0 7 _a o

i = 'oI , lo - o,T+t\ l

v .ote " \o ?^* t : t { 7"

'n16tt' -6 v ' ' ' ' � I I 59 t75-qo y*Scorei

6/ , rqmq€,,

Uah^Qt e...e- qpp -oX, ,/L<)( aais+; b,rte.l

o .v t P ( t - P ) -- lo,v (t-u'g)v trf

O , O 3 o L ' l

o - + + 1 1 - o . ? f ) 1 /

: - / o Q

o.rs 3 o L-4

? ( z ! 2 , s ) :o . L t + o . ooq+

l o o

5r^.a h*

ul< v-t e,t

Tvc./*<. ,6 o -ooL{ 7 iS l rsJ fLo'-t* oL=o'oa,

[+o i^ *^u ot*t o+ (+n , T-n"t-

S^ ??h ;e.,t eidanga 1T c-Dt cL,&e-

sa-hns$eo/ o* Tt+

nP?ai

C

--J4-fL@f | <

+1o (*

i 5

OvtJO O-h g"..-/ t

Scntu) t"*l%is

a,,<Jto"we-r S

ksS fra^ rf7, .

p. 11 o f 13

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OO7

Question 6 [10 points]: A car dealer recommends ihat new cars be brought in after the first

5000 km for tuning. A random sample of the records of 121 new vehicle customers shows that the

average mileage reading on the vehicles brought in for the initial tuning is 5037. The sample had

a standard deviation of 194 km. Is this sufficient evidence to conclude that, on average, customers

drive more than the recommended 5000 km before bringing their vehicle in for the initial tuning?

Test at the 0.05 level of significance. Clearly state the parameter you are testing as well as the null

and alternative hypothesis. Clearly state your conclusion.

L*t -A = MLkt+ a(lSf*<e e(n'.*r-" P^'u- *)

bv,,1:p co-r ( h. t.r. hl.t t*^E '

V =V \ =

5,-tc-b' 7 O P(-*,

t /14( *ui l

t1L{ a

l + , 6 y{F .iEi

2 " 1

= O ' o t + 1

r S

5

oA o

1es 5

fro-

+1o*-

. -fJe-re

s/ = (),of \ uJ< "j '"f

i t s ufh'ctet sia0t"^'Q-

t oA aue-4.^Je ) C*rSt av\a4 4'ri't+

S A W f u " b" {'n

i ^ ; *J tu ' -Z e

W LV"Vt*wl

vd^4 4'?J

et^oter/

tn +-

H o t f = S o o o

f t 3 , b

sD r+t a - l

/q. l

D ;sf u.'. b,*r'a,^

w; +1^. ,A=' / '

= t t l t ' o ) * =

T-/u OSD-l+- $u-D

1=.4

FV ( + . 6 Y

? - ""lr- : ? r e > 2 , 1 ) = , . ? ' l

t o ' )

5 , ^ , - ' o , o t T 1 ; 5

l-+o

to

/t42\a fla4^ /t'-e

; +^"cs,r Iqb ce"*[r fr"ct

bn',X;y 7'Ie) n

p. 12 of 13

Math 161 Sec F07N01 & F07N02 - Practice Final ExamDec 10 2OO7

Question 7 [10 points]: Some people are less willing to participate in surveys than others. Does

age have anything to do with this willingness to participate? Data from a survey on bank preference

is available: the following table gives data on individuals broken down by age group, and within

each age group, individuals were categorized as participating or not participating in the survey.

60 and over t+"(

did not

ro tfi

rs6

Is there sufficient evidence at the a : 0.05 level of significanc6 to con'clude that there is an association

between age and willingness to participate in the survey?

+o '. wo aS 5 o crc^Au-^ bel taee n "^3e.

, ?*-lic-t Palic-- b" Swt%J ..t*c^ j fl<-"e \ S a.\,\ qSS o Qoh ou,

1 L ' = 2e xpeiFea{

o

z(s+l - s>z,r) +.

r5?, t

l1 , f

d + = ( r - , ) ( c - , ) = ( r - \ ) ( j - r ) _ . L

C^hco! vo-b-q L^.1 1-"&'& a{.1 o*-rwspg,^oq' ,A4" I : a, c,{

o l+ = L i s t-11 -t

t,11 Lr<. *J ./ F[,r '4^ &-r,n *-

k- a-,v\ C*SSoc)aA a".. Lelt"eg-

S iuncr y'

n'<4<- &ps

= 1 1 , {

app€y h4 * l o '

202(ztt,s)

49( iz, f )

1 w ll t i2v.css +o

/ q e - , ' L

i . r + \ ' / , Z ' f )-

3 2 , i

"1" a.d L..r;(ti2r^esI *o p*t;?& ; Sqr""As

p. 13 of 13