(B) fo.z foro

32 Sample Exarnination Two Section E
6. If a 95% confidence interval is given by (86^52, 89.48), which of the following could
be a99o/o confidence interval for the same data?
L (86.98, 89.42)
II. (86.37,89.63)
III. (87,89)
(A) I only
(B) II only
(C) III only
(D) I and Ill
(E) II and III
7. Which of the following represents a probability density function?
(A) [0.0 for2

Section I Sample Examination Ttvo 33
8. Maritsa scored 82 on a geometry exam for which the class mean was 74 and the
standard deviation 3.2 and she scored 86 on a biology exam for which the class mean
was 77 rvith a standard deviation of 2.9.In comparison to other members of each of
these classes, which of the following conclusions can you draw?
(A) Her performance on the geometry exam was L:etter than her performance c,n the
biology exam.
(B) Her performance on the biology exam was better than her performanee on the
geometry exam.
(C) Her relative perforrnance was the same for both exams.
(D) Her relative performance was graded unfairly.
(E) No conclusion can be drawn frorn this data.
[-l
Answer
ll
9. Assurning that birthdays are uniformly distributed throughout the week, the probability
that trvo strangers passing each other on the street were both bom on Sulday is
(A) 1t7
(B) 2t7
(c) 1t4e
(D) 2t4e
(E) 4t4e
10. Which of the following are characteristics of a r-distribution curve?
l. The graph of a l-distribution extends infinitely to the left and to the right and
approaches the x-axis asymptotically as x increases in absolute value.
IL There are an infinite number of different /-curves, each determined by a
parameter called degrees of freedom.
Ill. The maximum point on the graph of a r-distribution occurs at its mean which
is always 0.
(A) I only
(B) II only
(C) Iil only
(D) I and III only
(E) I, il, and III
EAnswer
Answer
tt
tl
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34 Sample Examination Two Section E
ll' A teacher raised each student's grade by t0 points on an algebra exam. Which of the
following describes the correlation betu,een students' original srades and their adjusted
grades?
(A) slightly negatrve
(B) slightly positive
(C) close to 0
(D) -1
(E) I
12. In conducting a hypothesis test, thep-rralue is the
(A) probability of obtaining a result as extreme or more extreme than the one
obtained if the null hvpothesis is true
(B) significance level of the test
(C) probability of making a T1,pe I error
(D) probabilitv of making a T,vpe II error
(E) probability that the null h.vpothesis is true
13. In constructing a confidence interval based on a large sample to estimate the mean p
of a population with a knorm standard deviation o, which of the follon,ing does NOT
affect the rvidth of the confidence interval?
(A) the sample mean
(B) the popuiation standard deviation
(C) the confidence level
(D) the sample size
(E) the sample standard deviation
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Section tr
14. Which of the follov-'ing are conditions for a binomial experirnent'/
Sarnptre Examination Two 35
I. The number of trials n is a fixed number.
II. T'he n trials are independent.
IIi. The probabilifl of success p is equal to the probabilitS' of failure q'
(A) i only
(B) II only
(C) III oniy
(D) I and ll onl,r,
(E) I, II. and III
15. Which of the following is NOT true concerning sampling distributions?
Answer
r--]
ll
(A) If the sample size n is large, the sampling distribution of T, drawn from a normal
population, is approximately normal.
(B) The mean of the sampling distribution of p is equal to the population propor-tion
t)
(C) The mean of the sampling distribution of the difference of trvo means (x, - rr) is
equal to the difference of the population means (l'L'- llr).
(D) The standard deviation of the sampling distribution of I is (r1,6., where o is the
population standard deviation.
(E) The standard deviation of the sampling distribution of the differences of two
means 6x,-z.is equal to the sum of the respective population standard deviations.
Answer
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36 Sarnple Exarnimation Two Section I
16. The all-time leader in career bafting average among major league basebail players is Ty
Cobb with a career average of 0.366. This means he got a hit in 36.5oh of his official
at-bats. What was Cobb's probabiliry of getting at least one hit in four official at-bats?
(A) 0.092
(B) 0.134
(c) 0.162
(D) 0.366
(E) 0.838
17. Which of the folloiving accurately describes the polr,er of a statistical test of
hypothesis?
(A) It is equal to the p-value.
(B) It is equal to 1- (p-value).
(C) It is equal to d, the significance level.
(D) It is the probability that a test using a fixed value of s will reject H,, when a
particular alternative value of the parameter is true.
(E) It is equal to p.
Answer
Answer
I 8. The equation of the least squares regression line lor a set of points in a scatterplot is
given by i = 2.2+ 0.8lx. The point (5, 7) is one poinr on this scatterplot. Which of the
following is the residual for the point (5,7)?
(A) 0,71
(B) 0.7s
(c) 4.0s
(D) 6.25
(E) 7.87
or
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Answer

Section t Sample Exarnination T\vo 37
19. 'fhe table below shows the probability distribution for the number of tails (X) in five
tosses of a fair coin. What is E(X)" the exnected value of X?
(A) 2.0
(B) 2.5
(c) 3.0
(D) 3.5
(E) 4.0
X 0 I a J 4 5
D/ta\ 03125 r5525 .3r25 .3t25 15625 .03125
20" Which of the following statemen"ts is a consequence of the Central Limit Theorem?
I. If the original population is uniformly disstributed, then the sampling
distribution of x rvill be unifornt for large samples.
II. The sampling distribution of x will be approximately normal for large samples.
III. The mean of the sampling distribution of t will be close to I for large samples.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
21 " The probability of a tourist visiting an area cave is 0.70 and of a tourist visiting a nearby
park is 0.60. The probability of visiting both places on the same day is 0.40. The
probability that a tourist visits at least one of these two places is
(A) 0.08
(B) 0.28
(c) 0.42
(D) 0.e0
(E) 0.9s
EAnswer
Answer
Ansrver
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38 Samp[e Examination Two Section I
22. The correlation between height and weight among men betr,veen the ages of 18 and 70
in the United States is appro.ximately 0.42. Which of the folloivine conciusions does
NOT follow from the data?
(A) Talier men tend to be heavier.
(B) Changing the units of 'weight and height wouid stiil yieid the sarne correiation value.
(C) Heavier mell tend io be tailer.
(D) [f a man in this gloup ciranses his diet and gains ] 0 pounds, he is likeiy to get taller.
(E) There is a moderate association betn'een a il]an's height and weight.
23. A high school guidance counselor wishes to compare the PSAT results for the male and
female students in the junior ciass at your high school. \\'hich is the best technique for
gathering the data needed?
(A) census
(B) experiment
(C) observational study
(D) sample survey
(E) a double blind experiment
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Answer
[]
Answer

Section I Sample Examination Two 39
24. The stem plot below summarizes the number of gold medals earned by 40 countries in
the Winter Olympics for 1924-1998.
0 827990201 I 1001 101 10001000
l 988
2 9571
3 9895
43
59
6t
78
88
The data depicts a distribution that is
(A) skewed to the left
(B) skerved to the right
(C) symmetric
(D) uniform
(E) not determinable from the information given
Ansrver
25. A tire manufacturer claims that it has developed a new all-season radial tire for
passenger cars (excluding SUVs) which has a shorter skid distance than the known mean
skid distance, 140 feet, for all tires currently available. A consumer group wishes to test
this claim. If 1.2 represents the true mean skid distance for this new tire, which of the
following states the null hypothesis and alternative hypothesis that the consumer group
should test?
(A) H.: p < 140 ft. H,: lt > 140 ft.
(B) H": /1< 140 ft. H^: lt > 140 ft.
(C) H,: lt= I40 ft^ H^: /1< 140 ft.
(D) H": F = 140 ft. H^: P < 140 ft.
(E) H.: F = 140 ft' H^: F + 140 ft.
lAnswer
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4CI SarnpBe Examiuration Two Sectiom !
25. Suppose that A and B are events in a sample space with P(A) = 0.8 and P(Blal = 61.5.
Theri P(AandB) =
(A) 0.3
(B) 0.4
(c) 0.62s
(D) 0.8
(E) i
27 . A telephone survey of 1000 adult Americans ret eals the following data conceming the
President's tax cut plan
Support Oppose Undecided
Male 300 180 90
Female 2ra 190 30
Suppose a study is conducted to test the assoication between gender and position on the
tax cut plan. What is the expected number in the cell representing females who support
the tax cut plan?
(A) 210
(B) 21s
(c) 21e.3
(D) 240.3
(E) Not enough information given
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Section I Saenple Exarslinat[on Two 43
28. Two independent random samples of size nr= 45andnz= 38. r,vith respective standard
deviations 6r=2.3 and dz= 1.8, are drawn from trvo normally distributed populations.
Which of the follor,ving represents an estimate of the standard deviation of the sampling
distribution corresponding to xt- x2?
(A) 0.2s
rB) 0.31
(c) 0.4s
(D) 0.s0
(E) 2,05
29. SRS refers to a simple random sample. Suppose an SRS of size n is drawn from a
population. Which of the following accurately character\zes this sample?
I. It is a sample drawn in such a manner so that every set of n subjects in the
population has an equal chance to be the sample chosen.
Il. It is a sample drawn in such a manner so that every subject has some chance
of being chosen.
III. It is a sample drawn in such a manner that every subject in the population has
an equal chance of being selected.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
nAnsrver
Answer
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l'l Sample Examinaticn Two Section tr
30. The points (x, y) on a scatterplot form an
can be concluded aboul the correlation r
(A) r deueases in absolute value
(B) r increases in absoluie value
(C) r remains constant
(D) the value of r changes sign
(E) nc conclusion can be drarvn
ellipse. As the ellipse becomes thinner. what
between the variabies x and y'i
EAnsrver
31. The histogram below displays a set of measurements. Which of the boxplots belou'
disolavs the same set of measurements?
B
7
6
>.5 O-
C
Oi
l'
o
E3 LL
(A) -il- E
(D)
ffl-.-
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2
1
0
q
(B)
(E)
(c)
o
Answer

Section tr Sample Examination T\vo
32. The correlation r between the magnitude of an earthquake and the depth below the
surface of the earlh at which the quake occurs has been determined experimentally to
be about 0.51, Suppose we use the magnitude of the earthquake (x) to predict the depth
below the surface (y) at which the quake occurs. We can infer that
(A) the least squares regression line ofy on x has slope equal to 0.51
(B) the fraction of the variatioir in depths explained by the least squares regression
line ofy on x is 0.26
(C) about 5lYo of the time, the magnitude of an earthquake will accurately predict
the depth at which the earthquake occurs
(D) the numerical value of the depth is usually 51% of the numerical value of the
earthquake
(E) twenty-six percent of the data values lie on the leas{ squaies regression line
33. A report from the Maine Department of Inland Fisheries and Wildlife indicates that
there occurs on average one fatality per 100 collisions between cars and deer. In 300
collisions between a car and a deer, what is the expected number of fatalities and the
standard deviation?
(A) mean: 0.33 standard deviation : 0.01
(B) mean: 1 standard deviation : 0.01
(C) mean : 3 standard deviation : 1.72
(D) mean: 3 standard deviation :2.97
(E) mean: 30 standard deviation : 3.0
43
TAnswer
Answer
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Sample Examination TWo Section I
34. Johannes Kepler (1571-1630) was able to show that the square of the period of
revolution of a planet is proportional to the eube of its mean distance from the sun. The
equation y = 0.001118x''. where x is the distance of a planet irom the sun (in millions
of miles) and y is the period of revolution (in years) of a planet around the sun, is a
power regression model ivhich represents this relationslrip. Which of tire foiiowing lviii
produce a linear representation of this inodel?
(A) plotting y versers ln x
(B) plotting x versus ln x
(C) plotting x versus ln y
(D) plotting ln x versus ln y
(E) constructing the residuai plot for the scatterplot of y vs. r
3 5 . Which of the following is an appropriate graph to display univariate categorical data?
(A) stemplot
(B) histogram
(C) boxplot
(D) pie chart
(E) scatterplot
Answer
Ansrver
36. A large university is considering introducing a new major in Economic Geography and
wishes to poll the current student body for their opinion of the feasibility of introducing
such a rnajor. The Office of Public Relations mails a questionnaire on this issue to a
SRS of 2000 students currently enrolled in the university. Of the 2000 questionnaires
mailed, 532 have been returned of which2lg students supporl the new major. Which
of the following represents the population for this study?
(A) the 2000 students receiving the questionnaire
(B) the 532 students who responded
(C) the 219 students who support the nerv major
(D) the 2000 students selected represent a sample of the population of all currently
enrolled students
(E) all students who are currently enrolled and all past alumni of the university
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Section I Sample Examination Two
37. A Physicians' Study Group wishes to design a matched pairs test to determine the
effects of a medication on reducing the elevated cholesterol levels in 200 adults in the
35-65 age group. Which of the following represents such a design?
(A) The Physicians'Group compares cholesterol levels of each patient before he/she
begins a daily regimen of the medieine to the patient's cholesterol level after six
weeks of using the medication.
(B) The Physicians'Group compares the cholesterol ievels of tire patients using the
medicine for six weeks with the cholesterol levels of 200 aduits in the same age
group who exhibited elevated cholesterol ievels and did not take the medicine.
(C) The Physicians' Group compared the mean cholesterol level of the 200 patients
six weeks after using the medicine with a published national mean cholesterol
level for ali adults in this age group.
(D) The Physician's group compares cholesterol levels of the 200 patients using the
medicine for six weeks with the cholesterol levels of 200 adults in the same ase
group who were taking a placebo.
(E) All of the above are representative of a matched pairs design.
3 8. Let X represent the number of independent rolls of a fair die required to obtain the first
"2".What is P(X = 5)?
(A) (1/6)'(s/6)
(B) (1/6)4
(c) (s/6)'( 1/6)
(D) (s/6)'
(E) (5.6)'
Answer
Answer
45
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Sample Examination Tlvo Section I
39. A local university has a "drop-in center" located near the Student Union rvhere students
can "drop-in" to speak to a counselor on any issue or concern whether personal or
academic. A researcher stations herself at a receptionist's desk during a few random
evenings to collect data on whether men or women are more likely to use this service
and whether a particular class (freshman, sophornore, junior. senior) is more likely to
"drop-in." This study may be described as a
(A) controlled experiment
(B) matched pairs design
(C) census
(D) observational study
(E) a double blind completely randomized experirnent
40. A researcher wishes to use a 95o/o confidence interval to estimate the proportion of
Americans who have visited an entertainment theme park near Orlando rvithin the last
five years. The researcher rvishes to choose a size that will insure a margin of error not
to exceed 0.05. Which of the followins is the smallest size that meets these criteria?
(A) 40
(B) 200
(c) 400
(D) 600
(E) 800
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Answer
nAnswer

Section II Sample Examination TWo
Section II
Part A
Time-65 minutes
Questions 1-5
Percent of Section II srade-75
Directions: Show all 5rour work. Indicate clearly the methods you use, because you will
be gi'aded on the correctness of your method as well as on the accuracy of your results
and exnlanations.
L The table below shows the home run output of all Ameriean League and National
League baseball teams during the 2000 season.
American Leasue Home Runs
Cleveland
Kansas City
Chicago White Sox
Texas
Anaheim
New York Yankees
Detroit
Toronto
Baltimore
Minnesota
Oakland
Seattle
Boston
Tampa Bay
221
150
2t6
173
236
205
177
244
184
116
239
198
167
t62
National Leazue Home Runs
Colorado
San Francisco
Houston
Cincinnati
Atlanta
St. Louis
Pittsburgh
Montreal
Arizona
New York Mets
Florida
Los Angeles
Chicago Cubs
San Diego
Philadelphia
Milwaukee
161
226
249
200
t79
235
168
178
179
198
160
2t1
i83
(a) In the area provided below, construct one histogram displaying the distribution of
homerun output for all teams (both American and National Leagues). Describe
the nature of the distribution noting the center of the distribution, skewness, and
outliers (if any).
183
1AA
ITT
t77
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Sample Examination Two Section II
(b) Draw box plots for the data in each of the two leagues and identifl, the fivenumber
summary for each plot. What comparisons can you make between the
homerun outputs of the two ieagues?
(c) Construct a back-to-back stemplot displaying the homerun outputs of teams in
the two leagues,
or
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Section I Sample Examination Two
2. A telecommunications company uses three different systems to produce the print shaft
holder for its most popular fax machine. System A produces 50o/o of the shaft holders,
System B produces 30% ofthe shaft holders, and System C produces 20% ofthe shaft
holders. The percentages of defective shaft holders produced by each system are
respectively, 3Vo, 4Yo and 5o/o.
(a) If a shaft holder is selected at random, what is the probability that it is defective?
(b) If a shaft holder is selected at random and found to be defective, what is the
probability that it was produced by System A?
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50 Sample Exarnination Two Section [I
3. A Television Monitoring Group (TMG) claims that at least three out of every four
Americans believe that realitv-based television shorvs are untruthful. They tested their
claim by using data from a recent Gallup poll ufiich indicated that in a sample of 1 ,015
Americans, 812 thought the shows were either somewhat or totally untruthful.
(a) Testthe claim of theTMC using a signifieance level of 0.0i. State cleariy your
assumptions and u,hat test of hypothesis you are using. Identifu an appropriate
p-r'alue and interpret vour results ri'itiriir the context of the problenr.
(b) Construct a9SYo confidence interval to estimate the true proportion of Americans
who thinli these shows are essentially untruthful.
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Sectiosr II Sarnple Examination Two 51
4. A survey was conducted recently in ten large American cities to
there is any relationship between average weekday hotel rates and
rates. The followine data was collected.
Daily Hotel Rate (x)
(in dollars)
149
187
17l
r22
lt)
147
128
2r2
168
181
(a) Construct a scatternlot for this data.
(b) Use the scatterplot to determine if there
variables.
Daily Car Rental Rate (y)
(in dollars)
49
50
52
49
39
44
aa
JI
OJ
40
5l
determine whether
average car rental
is a linear relationshio between the tu'o
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52 Sample Examination Two Section II
(c) If there is a linear relationship, numerically describe the strength of this
relationship and construct a least squares regression model.
(d) Find tlie residual associated with the point (168, 46).
(e) What percent of the variation in car rental rates is explained by the regression of
yonx?
ol
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Section II Sample Examination Two
5. A medical research group is interested in comparing the effectiveness of two new
medications in reducing cholesterol levels in adult males ranging in age from 35-65
years of age who have exhibited elevated cholesterol levels for at least six months, Four
hundred men with elevated cholesterol levels in this age group were randomly selected
in New Ycrrk City and 340 men were randomly selected in Philadelphia. It is suspected
that results will differ greatly between the two cities due to a recent 'heart health'
initiative in Philadelphia. Describe a randomized block design to conduct this
experiment.
53
ot
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f,{ Sample Examination Two Seetion [I
Section II
Fart B
Time-25 minutes
Question 6
Percent of Section II erade-25
Direetions: Show'all your work. Indicate clearly the methods you use, because you wiil
be graded on the correctness of your method as rvell as on the accuracy of your results
and explanations.
6. In 1 908 W. S. Gosset wrote a paper titled, "The Probable Error of a Mean". in the paper
Gossett reported on the corn yieid using two different kinds of seeds. The first seed was
the usual seed used by farmers in England at that time. The second seed type was kilndried.
Each type of seed was planted in adjacent plots, accounting for 11 pairs of "split"
plots. The data are given belorv. The numbers are in pounds per acre.
Plot Regular Kiln-Dried
1 903 20a9
2 1935 1915
J 1910 2011
A
L+ 2496 2463
5 2 108 2180
6 1961 1925
7 2060 2122
8 441 t482
9 612 1542
10 316 1443
1t 5il 153 5
The following computer outputs show the descriptive statistics of the two variables and
a regression output which resulted from fitting a least squares regression line using
yield from "regular" seed to predict yield from "kiln-dried" seed.
Variable N Mean Medi-an TrMean StDev SE Mean
Regular 11 1841 191-0 1-827 343 t_03
Kiln-Dri 1l- 1875 L925 1858 333 t-00
Variable Minimum Maximum Ql- Q3
Regular l-31-6 2496 1511- 2060
xiln-ori L443 2463 1535 2L22
Predictor
onstrant
Ponrr'l rr
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Coef StDev
120 .4 LL6 .'l
0.95293 0.06241
R-Sq=l$.39 R-Sq (adj )
=95.98
T
1-.03
15 .21
P
0 "329
0. 000

Section trI Sample Examination T\vo 55
Below is a residual plot and a normal quantile plot of the residuals resulting from the
regression.
e
E
z
2
.2
Residuals Versus REGULAR
tesph3. is KLN-DRI)
rso 2@ 25m
REGULAR
Normal Probabili\i Plot of the Residuals
G.s@nse is KLN-oRl)
Residual
(a) Use side-by-side box plots to compare the corn yield for the two groups. Write a
few sentences commenting on your display.
(b) Can yield of "regular seed" be used to predict the yield of "kiln dried seed"?
Give statistical justification to support your response.
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Sample Examination Two Section Itr
(c) Is there a difference in yield betu,een the two types of seeds'/ Give statistical
justification to support your response.
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