SampHe Exaxmixnati*rs Six - La Jolla High School

SampHe Exaxmixnati*rs Six
Section I
lirne-l hour and 30 miuutes
Questions 1*40
Percent of total grade-S0
Dfrections: The quesiions or incompiete statements that foliou,are each followed by five
suggested answers or eompletions. Choose the response that best ansu,ers the question or
cornpleies the statement.
l. A random sample of 100 people '.^,,as asked to state his or her gender and favorite ice
cream flavor. The results appear in the table belou,.
Male 10
Female
Vanilla Chocolate Strawberry
aA
LA t2
ao
LO 16 10
A chi-square test is used to test the null hypothesis that gender and preferred ice cream
flavor are independent. Which of the following statements is correct?
(A) Do not reject Ho at the 0.05 significance level.
(B) Do not reject Ho at the 0.01 significance level.
(C) Reject Ho at the 0.01 significance level.
(D) Reject Ho at the 0.005 significance level.
(E) Reject Ho at the 0.001 significance level.
2. If a null hypothesis that is actualll, false is not rejected, we have
(A) made a type I error
(B) made a type II error
(C) made neither a Type I nor Type II error
(D) obtained a sample that is definitely biased
(E) chosen a null hypothesis that cannot be tested
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Section I Sample Exarninatiom Six
3. T'he probability that a child will have a problem with alcohoi is 0.75 if-at least one of
tl-re parents is an alcoholic and 0.05 if neither parent is an aicoholic. in a recent study
of a large number of children , SYo of the children involved had at least one parent who
is an alcoholic. If a chiid in ilris study has an alcohol-related problem, what is the
probability that at least one of the parents of the child is an alcohoiic?
(A) 0.0375
(B) 0.047s
(.c) 0.4412
(D) 0.78es
(E) 0.8000
4. The November 2000 Presidential election had George W. Bush and Albert Gore as the
2 major candidates. Suppose thatZl3 of the people in the city supported Bush but 5/9
of the people in the suburbs supported Gore. 60% of the people live in the city while
40Yo of the people live in the suburbs. If you select a random Bush supporter, what is
the probability that the person lives in the city?
(A) 1e.8%
(B) 30.8%
(c) 34.6%
(D) 66.7%
(D 69.2%
r3r
Answer
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1?t Sample Exax'ninaticn Six Seetion I
5. Consider the folloq,ing test scores:
Class A: 65,72,73,73,74, 82, 9l Class B: 60.65.79,81,85,86, 86
Which of the following is a true statement?
(A) Class A has the greater range, while Class B has the greater standard deviation.
(B) Class ts has the greater range, ra'hile Class A has the greater standard deviation.
(C) Tlie ranges and standarC deviations are the same for both classes.
(D) The ranges are the same, but Class A has the higher standard deviation.
(E) The ranges are the safite, but Class B has the higher standard deviation.
6. The verbal scores of incoming freshmen at a large university are approximately
normally distributed with a mean of 550 and a standard deviation of 100. The
administration wishes to give an honors English course to the top 5Yo of the freshmen.
What is the minimum score that must be attained to qualify for the course?
(A) s50
(B) 600
(c) 66s
(D) 71s
(E) 74s
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Section I Sarnple Exarnination Six
7 ^ The correlation coefficient is
(A) a number between -1 and +l that measures the strength and direction of the
linear relationship between two variables
(B) a positive nurnber that measures the goodness of fit
(C) always equal to the slope of the regression line
(D) never equal to zero
(E) the fraction of the variation in the values of y that is explained by the leastsquares
regression ofy on x
8. A researcher wishes to examine the relationship between years of schooling completed
and the number of pregnancies in young women. Her research discovers a linear
relationship, and a least squares fit of her data results in the model
v=6.4-0,12x
where x is the number of years completed in school andy is the number of pregnancies.
What is the estimated change in the number of pregnancies that corresponds to the
completion of an additional 10 years of school?
(A) a decrease of 5.2
(B) an increase of 7 .6
(C) a decrease of 7 .6
(D) an increase of 1.2
(E) a decrease of 1.2
r33
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134 Sarnple Exarnination Six Section E
9. What is the effect on the correlation betr.r,een trvo variables ( x, t,) if each r-value is cui
in half and 0.04 is subtracted from each v-value?
(A) 'rhe
(B) The
(C) Ihe
(D) The
(E) The
colrelation is cut in half.
correlation is decreased b"v 0.04.
correlation is decreased by 0.0016.
correlation is unchanged.
correlation is doubled.
10. A major tire manufacturer claims that his shock absorbers last for 5,000 miles. A
consumer watchdog group claims ftat the actual mileage is lower. If 7: represents the
true average life of the shock absorbers, rvhich of the follou'ing are the appropriate null
and alternative hvpotheses?
(A) Ho:l= 5000
(B) Ho:p< 5000
(C) Ho:tr7= 5000
(D) Ho:p> 5000
(E) Ho:,U= 5000
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H":1t< 5000
Ho /t+5000
Hu: trt+5000
H": trt+5000
Hu: trt> 5000
Answer
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Section I Sampie Examination Six 135
ll. Which of the following are true statements?
I. A census aims to obtain information about an entire population by studying a
smail sample of the population.
il. Sample surveys are experiments.
IIL A treatment is imposed in an observational study.
(A) I only
(B) II only
(C) Itl only
(D) If and III
(E) None of the above
Answer
12. Aresearcher plans a study to examine the attitudes of residents of Califomia towards a
proposal in Congress to declare English to be the official language of the state. He
obtains a random sample of 50 residents of one community in California and all agree
to participate. Which of the following statements is true?
(A) This is a poorly designed survey because it is a voluntary response sample.
(B) The design of the study may be biased because the sample may not represent the
population of interest.
(C) It is a well-designed survey because of the 100% response rate.
(D) As long as the respondents were randomly selected, there is no bias.
(E) A more accurately designed study would have included opinions on this issue
from residents in other states.
Answer
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tJb Sarnple Examination Six Section I
13" The age of {.Jnited States Fresidents at
cumulative proportions graph. What is ihe
(A) 2
(B) 8
(c) i2
(D) ls
(E) 2s
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H
o
r)
1.00
.90
.80
.60
.50
.44
.30
')n
.10
their inaugurations rs
approxi m ate interquarli ie
39.5 11.5 49.5 54.5 59.5 64.5 69.5
Age
dispiayed in this
rarrge (IQR)?
Answer

Section I Sample Examination Six -tJ /
14. In testing the design of a new tennis racket, a company randomly selected 12
professional tennis players and counted the number of aces each player served when
using each racket in a 2-minute period. The resurts are as follows:
What is the number of degrees of freedom associated with a l-test to determine if there
is a difference between the number of aces served using the 2 rackets?
(A) 6
(B) 10
(c) l1
(D) 12
(E) 24
Flayer Racket #1 R.acB

138 Sarnple Examination Six Section tr
15. Evan and Am1, are t$,o seniors in a local high school. The grades on a Calculus final
which Evan took weie approximately normally distributed with a mean of 75 and a
standard deviation of 7. The grades on a Fsycholog.v final rvhich Amy took were also
approximatell, nonnallS' Cistributed .,vith a mean of 85 and a standard deviation of 4.
Evair scored an 89 on the Calcuius finai while Arny scored a 91 on the Psl,chology final.
Relative to tl-re students in each class. u4ro did better on the final?
(A) Evari
(B) Amy
(C) Both r,r,ere the same
(D) You canaot compare a matlr course to a science course
(E) There is not enough information to ansrver this question
16. The distribution of lengths of boa constrictors is approximately normalll'distributed. If
11.5% of these snakes are more than 147 inches long and 2.3o/o are less than 139 inches
long, what are the mean and variance of tl-re lengths of boa constrictors?
@) It= 142,o2= 4.72
(B) p=143,o2=2.5
(c) lt= 143,o2 = 6.25
(D) lJ = 144,O2 = 2.5
(E) p= 144,o2 = 6.25
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Section I Sarnpte Exarnination Six tr39
17. Whioh of the following are true statements?
L The alternative hypothesis is two-sided if deviation from the null h1'pothesis
is relevant in either direction.
IL Hypothesis tests are designed to measure the amount of evidence that exists
against the alternative hypothesis.
IIi. A well pianned test of hypothesis eliminates the need for a control group in an
experiment.
(A) I only
(B) iI only
(C) III only
(D) I and III only
(E) I, II, and III
18. Two different methods of teaching French are under consideration. In the first rnethod,
a public television program is shown to the class, and a teacher spends the rest of the
period revierving the concepts viewed in the program. In the second method, a textbook
and traditional teaching methods are empioyed. After a period of time, an exam is
administered to allthe students. The test scores of the 21 students in the first class had
a standard deviation of 11.01 and the test scores of the 23 students inthe second class
had a standard deviation of 17. 15. If the difference between the mean test scores of the
2 classes is 9.95, is there sufficient evidence to conclude that there is a difference
between the methods?
(A) We cannot draw any conclusion rvithout knowing the means of the individual
classes.
(B) There is sufiicient evidence to conclude that there is a difference between the
methodsatd=0.05
(C) There is sufflcient evidence to conclude that there is a difference between the
(D)
(E)
Answer
methodsatd=0.01
There is insufficient evidence at a = 0.05
Since the sample sizes are different, we cannot perform any statistical analysis.
Answer
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140 Sarnple Examination Six Section tr
19. The Central Liniit Theorem of statistics states which of the fotlowing for a sample of
size n, (n > i),
(A) the si,ape of the sampling distribution of sample rneans is always normal
(B) the mean of the set of sample means is always less than the mean of the population
(C) the standard deviatiern of the set of sample means is equal to the standard
deviation of the population
(D) the mean of the set cf sample means is equal to the mean of the population rvhen
n is large
(E) the standard deviation of the set of sarnple means is greaterthan the standard
deviation of the population
20. George Washington High Schooi has a distribution of grade point averages which are
approximately normally distributed with a mean of 2.5 and a standard deviation of 0.5.
All students q'ith a 3.5 or higher grade point average graduate with honors. According
to the Empirical Rule, approximately rvhat percentage of the students will graduate
nith honors?
(A) 2.5%
(B) 59'o
(c) t3.s%
(D) 16%
(E\ 9s%
2l. lf X is a normally distributed random variable with a mean
deviation of 4, then P (14 < X < 82) is
(A) 0.1e1s
(B) 0.2417
(c) 0.4332
(D) 0.6247
(E) 1.0000
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of 80 and a standard
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Section I Sample Examination Six
22' The mean of a set of'data is 40 pounds and the standard deviation is 8 pounds. What
value of an observation corresponds to a z-score of _1.25?
(A) -30
(B) -s0
(c) 30
(D) 32
(E) 50
23. Suppose you select a random sample of size 5 from a normal distribution with unknown
mean /l and unknown variance 02. The null hypothesis Ho:/t=65 is to be tested
against the alternative hypothesis Hu:H#65 atrr,= 0.05. If the resulting sample mean
is 68'25 and s2 = 9, what is the value of the appropriate test statistic and the conclusion?
(A) 1.96; reject Ho
(B) 2. 132; reject Ho
(C) 2.132; do not reject Ho
(D) 2.a2; reject Ho
(\ 2.a2; do not reiect Ho
24. A die was rolled 24 times with the followins results:
Number of dots I 2
a
J 4 5 6
Frequency 2 8 2 J 8
A goodness-of-fit chi-square test is to be used to test the null hypothesis that the die is
fair. At a significance level of d =.01, the value of chi-square and the decision reached is
(A) 12.5; do not reject the null hypothesis
(B) 12.5; reject the null hypothesis
(C) 25.0; do not reject the null hypothesis
(D) 25.0; reject the null hypothesis
(E) 75.5; reject the null hypothesis
t4t
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42 Sarnple Examination Six Section E
25. A study found that playing classical music increased worker productivity. Horvever, the
researchers were not aware that the workers knew about the study while it rvas in
progress. Since the increase in productivitl may have been due to the workers'
knowledge that they were being studied, this is a potential example of
(A) the control group effect
(B) the effect of a treatment unit
(C) a lurking variable
(D) sampling effor
(E) voluntary response bias
26.The regression line of a set of data is y=2x+b which passes through the point (3,5).
If x and y are the sample means of the x and y values, respectiveiy, then
(A)
(B)
(c)
(D)
rtr)
j= 2t+ 6
n-.4
J= zx+ I
l-L^
l=u
y=x+o
27. A straight line of the form y-- a+ bx is fitted to the 5 data points (1, 0), (0, 3), (3, 1),
(2,-3), and (4,2) by the method of least squares. What is the value of 6?
(A) -3
(B) -2/3
(c) -1lr0
(D) 4/s
(E) 4
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Section I Sample Examination Six 143
28. 'rhe average number of pushups a united states Marine does daily is
standard deviation of 50. A random sample of 36 Marines is selected.
probability that the sample mean is at most 320 push_ups?
(A) 0.0082
(B\ 0.3446
(c) 0.6554
(D) 0.8767
(E) 0.9918
300, with a
What is the
Anslver
29' Which of the following statements regarding inference procedures for a population
mean are true?
JU.
I' The data should be a simple random sample of size n drawn from the population.
Il' When using a r-distribution, we generally assume the data are drawnfrom a
population that has a normal distribution.
III' We use a r-distribution rvhen the population standard deviation is unknown.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and IIi
Find the standard error of the mean for a distribution where samples of size 64 are taken
from a population with a mean of r14 and a standard deviation of 16.
(A) 0.5
(B) 2.0
(c) 3.0
(D) 16.0
(E) 18.0
rAnswer
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144 Sample Examination Six Section I
31" When a national magazine rated a particular university as its choice for the #1 schooi
in the nation, it stated the average salary of its graduates. The distribution of salaries
was unimodal and skewed right. Later it was determined that the figure stated rvas
inflated due to the salary of one alumnus whose income was considered an outlier. If
the outlier is removed' which of the follou'ing rvould defirtite!}'remainthe same?
(A) mode
(B) median
(C) range
(D) variance
(E) standard deviation
32. Which of the following is a correct statement?
(A) An event that is certain not to happen has a probability of 1'0.
(B) Probabilities are numbers whose values can be any number from -l to 1.
(C) The total of the probabilities assigned to all outcomes in a sample space must be
exactly 1.0.
(D) Probabilities are always rvhole numbers.
(E) If two events are dependent, then the probabiliqv that both events occur is the
nroduct of their individual probabilities'
33. Michael and Jeffare scheduled to take their midterrn exam in statistics. The probability
that Michael will pass is 0.40 and the probability that Jeffwill pass is 0.60. If the two
events are independent, which statement is correct?
(A) The probability that exactly one passes is 0.0576.
(B) The probability that exactly one fails is 0.52.
(C) The probability that they both pass is 0.20.
(D) The probability that they both pass is 1.0'
(tr) The probability that they both fail is 1'0.
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Section I Sample Exarnination Six l4S
34. Find the value of'the appropriate test statistic for the given hypothesis test.
Ho, trt = 59.2
H^,1t*58.2
cr = 0.01
(A) -4 50
(B) - 1.12s
(c) -0.281
(D) 1.r25
(E) 4.s0
x = )o,6f
s = 4.80
n= 16
35. The graph below is constructed from data drawn
distribution. Which set of frequendies could match
0 < X < 2,2

146 Sarnple Examination Six Section E
36. R-efer to the fbllorvins back-to-back stem-and-leaf plot:
Wirich of the folloiving are true?
9BB7 7 7
100
z
4
0
5i
222
U
I
2 a
A
+
i
5
,7
G
22
34556
11C)
I lal
4
2s 67
0
I. The medians of the distributions are the same.
II. The averages of the distributions are the same.
III. The ranges of the distributions are the same.
(A) I only
(B) II only
(C) IiI only
(D) I and II
(E) I and III
37. An association wishes to design and conduct a poll to determine the proportion of
Americans rvho oppose a lau, limiting the sale of handguns. If they rvish to be 98o/o
confident that their sample results differ from the true population proportion by no more
than 0.07, which of the following choices is the smallest sample size they should use?
(A) 1s6
(B) 215
(c) 2s0
(D) 300
rE) 500
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I an
t+ t Seetion ! Sarnple Examination Six 147
38. A linear model was constructed for a set of bivariate data using least squares regression
techniques. Given the residual plot shornn, what conclusion should be drawn?
(A) A linear model was not a good fit for the data.
(B) A linear model was a good fit for the data.
(C) The correlation between tl-re original variables is close to 1.
(D) The data was drau.n from a population that was not nomally distributed.
(E) The study was poorly designed.
39. A survey was conducted to determine the average age at which college seniors hope to
retire. In a simple random sample of 101 seniors, 55 was the average desired retirement
age. with a standard deviatior-r of 3.4 years. A 96% confidence interval for desired
retirement age of all college seniors is
(A) 54.30 to 55.70
(B) 54.55 to 55.45
(C) 54.58 to 55.42
(D) 54.60 to 55.40
(E) 54.63 to 55.37
Answer
Answer
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i48 Sample Exaxnination Six Section I
,t0. Which of the follo.wing examples satis| the requirements of a binomial seffing?
I. A football coach is trying tc decide which of his 3 quarterbacks to start in the
opening garne of the regular season. Last year's record shows that the number
of passes completed b3, one of the quarterbacks improves as the season goes
on. The coach is trying to determine the probability of that player completing
9Aok af his passes during the flrst game.
II. in fighting the West Nile \iirus. the EPA is concerned about hor.v much
pesticide residue remains iir Central Park the rnorning after an aerial spraying.
'fhe,v take grass cuttings from different sections of the park and measure the
pesticide residue.
ili" On "The Price is Right", a contestant can rvin a car in a game that involves
selecting cards that contain 2-digit numbers. There are 9 cards to choose from,
each with tq,o digits. The object of the game is to pickthe 2 cards that
represent the first 2 digits and the last 2 digits of the price of the car. She has
up to 5 chances to pick a card. Each time a card is chosen, it is removed from
the game.
(A) I only.
(B) II only
(C) III only
(D) All of the above
(E) None of the above
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Section Itr
Fart A
Time-65 minutes
Questions l-5
Percent ofSection II srade-75
Dirqclisns: Show all your work. Indicate clearly the methods you use, because you will
be graded on the correctness of your method as well as on the accuracy of your results
and explanations.
l. The motor vehicle bureau claims that 42oh of all new cars are Sport Utility Vehicles
(SUV)" Police Department sources feel that the true proportion is actually higher. To
check this claim, the police department randomly sampled new car dealers and found
that 95 out of 200 new cars were SUV's.
(a) Is there sufficient evidence to reject the motor vehicle bureau's claim at the 0.10
level of sisnificance? Show all work.
(b) Find a 95oh confidence interval for the true proportion of new car owners having
SUV's. Interpret this interval.
L49
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15fi Samp[e Exarnination Six Section Itr
2. A conscientious political science major gathered the follorn'ing data froin a random
sample of college fieshmen.
Political Farty vs. Gender
Dernocrats R.epublicans Others Totals
F ernales 22 1A t7 63
MaIes 16 t2 7
Totals 4A 36 a^ 100
Do the data provide evidence of an association between political party afhliation and
gender in freshmen at the 5% level? Give appropriate statisticaljustification.
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Section II Sample Examination Six 151
3. The graph below displays
for two Alsebra II ciasses.
cum f
i.00
.80
.60
.40
.24
t0
20
(a) Find the median grade
the cumulative relatrve frequencies ofthe final exam grades
onehonors( )and one college Frep (- - = ).
30 4A 50 60
for each class.
Grades
(b) Find the interquartile range for each class.
(c) Drarv parallel boxplots for both Algebra II classes. What conciusions can you
draw from the boxnlots?
70
BO
90
r00
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152 Sarnple Exarnination Six Section EI
4. A game spinner has four equal sections colored red. yellow. green and blue. The poirrt
values of each color are 4,3,2 and I respectively. you spirr twice.
(a) v/hat is the probability that the surn of your points is an even nunrber?
(b) \Vhat is the probabilify that the sun: of your points is an odd n,;mber?
(c) You rvin the game if the sum of your spins is a 2 or an 8. What is the probability
that you win the game?
(d) If the sum of your spins is a 2 or an 8, you win $ 100. You win $50 if the sum of
your spins is a 3 or a7,$24 if the sum is a 4 or a6 and $10 for a sum of 5.
Compute the expected value of tl-re amount you could u'in.
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Section II Sanonle Exarnination Six 153
5. Ronald scores 700 on the math section of the SAT exam. l"he distribution of'SAT scores
is approximately nonnal with a mean of 500 anda standard deviation of 100. Rubin
takes the ACT math exam and scores 31 on the math portion. ACT scores are
approximateiy normaily distributed r.r,ith a mean of 18 and a standard deviation of 6.
(a) Reiative io their peers rvho aiso took the tests, who pei'fbrmed better on his test?
Explair-r.
(b) A certain school will only consider those students who score in the top I % in the
math section. What grades would Ronald and Rubin have to receive on their
respective tests to be considered for admission?
(c) Between what trvo grades does 95% of the population fall for the ACT and the
SAT exams?
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Section II
E rtg
Time-25 minutes
Question 6
Pereent of Section I{ erade-25
Directions: Show all your u,ork. Indicate cleariv the methods you use.
be graded on the conectness of -1,6u. method as rveil as on the accLlracv
and explanations.
AP Statistics Data
Student Annual Grade AP Exam Grade
90 3
2 92 5
3 90 I
4 88 A-
5 67 2
o 82
(a) Represent this data on a scatterplot
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7 90 2
8 83 J
9 74 +
10 82
,
+
tl 90 A a
T2 t7 3
IJ 90 J
t4 91 5
15 96 5
!)
tr
r '')
X
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154
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Section II Part B Sample Examination Six
(b) F'ind the equation of the least squares regression line for predicting AP Exam
grade based on annual grade. Interpret the slope estimate. Also find the value of
the correlation coeffi cient.
(c) Draw the residual plot. Does your plot indicate that this is a good linear fit?
Explain.
(D) Find the value of r' and explain its meaning in the context of these data.
(E) Find the mean and the standard deviation of the annual grades and determine
whether the data satisf, the Empirical Rule at one standard deviation. What do
your findings imply? Are your findings supported by a graph of the data or by
any characteristics of the data? Explain"
155
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