Download PERDI questions 2

The Game of
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Preparing for the A.P. Statistics Exam with Problems in
Probability
Experimental Design
Regression
Descriptive Stats
Inference
Version 2
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PERDI – Version 2
Acknowledgments
Graphics in this manual were produced from:
1. Texas Instruments TI-Smartview Emulator Software for the TI-84.
©Texas Instruments, Inc.
2. InTaglio ™ software. [email protected].
3. Equation Editor Software for the Mac. © Design Science Corp.
4. Grapher Software: © Apple Computer Corp.
5. Fathom 2.0 Dynamic Data Software: © Key Curriculum Press.
Thanks to my partner Ted Tyree for his unwavering support in all of my
projects and his monumental work in bringing my materials free to
anyone who wants them through the Internet.
Full appreciation to Tim Greer for doing every problem checking for
errors and looking at every possible way a student could misconstrue its
meaning.
If you do find errors or have any questions or comments, please direct
them to: [email protected].
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PERDI – Version 2
P – 1 – Version 2
A radio-talk show has a promotion on its weekend shows. People call in
and if they are chosen to talk on the phone, they are eligible for a prize.
The mangers of the station estimate that the probability of winning a
prize on either Saturday or Sunday is the same. It is possible to win on
both days as well – the days are independent. If the probability of
winning at least one prize is 50%, what is the probability of winning a
prize on Saturday?
A) 20%
B) 25%
C) 29%
D) 32%
E) 50%
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PERDI – Version 2
P – 2 – Version 2
The Eagles and Cowboys played a number of games this year and are
playing each other in the last game of the year. Statistics for the year
show the following:
When the Eagles offense gets the ball, it scores a touchdown (7 points)
15% of the time and a field goal (3 points) 23% of the time. The rest of
the time it doesn’t score. It gets the ball on average 9 times a game.
When the Cowboys offense gets the ball, it scores a touchdown (7
points) 20% of the time and a field goal (3 points) 26% of the time. The
rest of the time it doesn’t score. It gets the ball on average 8 times a
game.
If we only consider offensive scores, what would be the expected score
for the game to the nearest point?
A) Cowboys 19, Eagles 17
B) Cowboys 41, Eagles 34
C) Cowboys 17, Eagles 16
D) Eagles 21, Cowboys 19
E) Eagles 20, Cowboys 20 (Tie)
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PERDI – Version 2
P – 3 – Version 2
(based on a true story)
The Tyree family loves Cheerios and eats them every morning for
breakfast. They consider themselves aficionados of Cheerios and claim
that there is a difference in taste between the Cheerios in the small box,
medium box, and large box. A friend of the family came to
Thanksgiving dinner and decided to investigate their claim. She filled
three bags with Cheerios, one bag from the large box, one bag from the
medium box, and one bag from the small box. Every member of the
family (12 people) were asked to rate the Cheerios in taste and decide
which came from the large box, which came from the medium box, and
which came from the small box. After everyone had submitted their
order, the answers were given. It turned out that 3 of the 12-person
Tyree family got the order correct. What is the probability of this
occurring by chance and what conclusion can you make from this
survey?
A) P = .005
There is good evidence that the Tyree family
B) P = .005
knows their Cheerios.
There is not enough evidence that the Tyree family
C) P = .197
knows their Cheerios.
There is good evidence that the Tyree family
D) P = .197
knows their Cheerios.
There is not enough evidence that the Tyree family
knows their Cheerios.
E) The sample is too small to make a conclusion.
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PERDI – Version 2
P – 4 – Version 2
Examine the function f ( x) on the diagram below defined on the interval
[-2, 2]. The height of the triangle is 0.5. Which of the following
statements is true based on this function?
!
A) P("2 # x # 1) =
7
8
B) P("2 # x # 1) =
3
4
C) P("2 # x # 1) =
5
8
D) P("2 # x # 1) =
5
6
!
!
!
E) f ( x) could not be a continuous probability density function.
!
!
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PERDI – Version 2
P – 5 – Version 2
A binomial distribution has probability of success .45 with 55 trials. If
the number of trials decreases by 10 and the probability of success
increases by .10, what is the effect on the mean and standard deviation
of the two distributions?
A) The mean and standard deviation both increase.
B) The mean stays the same but the standard deviation decreases.
C) The mean increases but the standard deviation stays the same.
D) The mean and standard deviation stay the same.
E) The mean and standard deviation both decrease.
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PERDI – Version 2
E – 6 – Version 2
A simple random sample of 100 students allergic to milk in Newton
County was taken. 40 of them were found to have a calcium deficiency
when compared to the recommended daily requirements for teenage
children. Which of the following is a valid conclusion from this study?
A) Roughly 40% of Newton County students have calcium deficiencies.
B) Milk allergies cause calcium deficiencies in 40% of Newton County
students.
C) Newton County students should take calcium supplements.
D) Drinking milk provides more calcium.
E) No conclusion is valid.
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PERDI – Version 2
E – 7 – Version 2
A study to determine whether men or women talk more to comfort their
dogs in a particular city was conducted in the following way:
A simple random sample of veterinary offices in that city was taken. A
hidden microphone was placed in the treatment room and the adult was
left alone for several minutes with his or her dog. Every 5th person was
secretly overheard and determined whether he or she talked or did not
talk to their dogs in the time they were alone. Data from the sites were
compiled and a two-way table was generated.
What kind of problems might arise from conclusions from the study?
A) Results could be confounded by the type of dog.
B) This is systematic sampling.
C) There is under-coverage present.
D) There is too great a possibility for non-response.
E) None of these errors occurred in the study.
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PERDI – Version 2
E – 8 – Version 2
Root canal is stressful to patients. There is thought that some ways to
reduce the stress (lower blood pressure – BP) is to allow patients to
watch their favorite TV shows during the procedure. There are other
people who believe that putting the patient in a light sleep during the
procedure will reduce stress. Suppose an experiment is set up and it
takes the form below (with the control group taking the traditional
Novocain). What is the design of the experiment?
A) Blocking for the type of root canal treatment
B) Blocking for gender
C) Matched pairs design
D) Stratification
E) Multi-stage
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PERDI – Version 2
E – 9 – Version 2
A population of 800 workers in a mall are 60% women, 40% men. Each
worker is given a 3-digit number. A researcher needs to take a random
sample of 20 people for a survey. He uses the random number table
below and examines 3 digits at a time.
Which of the following assignments of digits is appropriate in choosing
the random sample according to the mall’s demographic?
55882 38465 98730 24522 97660 00408 38418 73332 84651 …
A) 000 to 480 = women, 481 to 800 = men, ignore the others
B) 001 to 480 = women, 500 to 820 = men, ignore the others
C) 000 to 319 = men, 520 to 999 = women, ignore the others
D) 000 to 239 = women, 240 to 399 = men, ignore the others
E) 000 to 320 = men, 321 to 799 = women, ignore the others
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PERDI – Version 2
E – 10 – Version 2
Every year around the Christmas holidays, a giant cable company with
millions of customers contacts a number of their customers to find if
they are happy with their service. This year, because of the cost
involved, the company cuts in half the sample size. The result of this
cutback will most probably
A) increase non-response bias.
B) increase the effects of any confounding variables.
C) increase the standard deviation of the sampling distribution.
D) increase the variability in the population.
E) have little effect because of the large population.
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PERDI – Version 2
R – 11 – Version 2
A method of rating tsunamis (tidal waves) in terms of their destructive
force is on a scale of 1 to 5 with 5 being the most destructive. Suppose
data is collected over time in the form (destructive force, damage) of
various tsunamis. Because the damage of large tsunamis is so extensive,
the data is transformed. The linear regression model of the transformed
data has the equation:
log(Damage) = 2 + .5 " Destructive force
What is the regression model of the original data?
A) Damage = 2 " 5Destructive force
B) Damage = 2 " 3.16Destructive force
!
C) Damage = 100 " 3.16Destructive force
!
D) Damage = 100 " 5Destructive force
!
E) Damage = 3.16 "10Destructive force
!
!
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PERDI – Version 2
!
R – 12 – Version 2
Which of the following is not true regarding linear regression?
A) The least-square regression line always passes through the point
( x ,y ) .
B) Regression yielding an r value of -.8 is stronger than regression
yielding an r value of .6.
C) A residual showing no clear pattern is an indicator that linear
regression is a good fit.
D) 68% of the data points lie within one standard deviation of the point
( x ,y )
E) All of these are true.
!
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PERDI – Version 2
R – 13 – Version 2
In the town of MathPro, everyone is excellent at math. On the platforms
of MathPro’s subways, there is a sign:
Want to estimate how long your trip will take you? Let s be the number
of subway stops your destination is from here and t be the amount of
time in seconds to reach your stop. Use this formula:
t=89.2s"13.4
r=.87
This formula is the result of a least-squares regression found with a
! trains. A trip of 12 subway stops took me 16 minutes
sample of subway
and 30 seconds. What is the residual of the time for my trip in minutes
and seconds?
A) approximately negative one minute and 7 seconds
B) approximately positive one minute and 7 seconds
C) approximately negative one minute and 31 seconds
D) approximately positive one minute and 31 seconds
E) approximately negative one minute and 12 seconds
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PERDI – Version 2
R – 14 – Version 2
A veterinarian is doing a study on the lengths of cats at different ages.
He examines 20 cats at different ages (x) and finds their lengths in
inches (y). The vet attempts two regressions.
Regression A yielded
"
log y=2.13log( x)#.021 and had the following residual plot:
Regression B, yielded
"
log y=.43x#.45 and had the following residual plot:
Describe the relation between x and y and which gives a better fit.
A) Linear, A
B) Power, A
C) Power, B
D) Exponential, A
E) Exponential, B
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PERDI – Version 2
D – 15 – Version 2
Which of the following would be useful in determining the IQR of a
distribution?
I.
II.
III.
IV.
histogram
cumulative proportion plot
stemplot
boxplot
A) I and III only
B) III and IV only
C) III only
D) II, III, and IV only
E) I, II, III, and IV
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PERDI – Version 2
D – 16 – Version 2
If each value of a data set is increased by 50%, then the variance of the
new data set will
A)
B)
C)
D)
E)
remain unchanged
increase by a factor of 50%
increase by a factor of 25%
increase by a factor of 100%
depend on the actual data
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PERDI – Version 2
D – 17 – Version 2
A certain model car sells on average nationwide at $19,525. About 12%
of the dealerships in the country sell the car for above $20,000. What is
the approximate standard deviation of the nationwide prices for this car,
assuming normality of prices?
A) $404
B) $20
C) $57
D) $418
E) depends on the number of dealerships
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PERDI – Version 2
D – 18 – Version 2
Students enter their essays in a contest in order to compete for a prize.
Each essay is read by the same number of judges. Doug’s essay has a
different score from each judge. If the lowest score and the highest score
for Doug are both eliminated, which of the following would definitely
change?
I. The mean
II. The median
III. The standard deviation
A)
B)
C)
D)
E)
I only
II only
III only
I and III only
None will change.
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PERDI – Version 2
D – 19 – Version 2
The average height of workers in a large corporation is 5’8”. 15% of the
workers are over 5’10”. Approximately what percentage of workers are
over 6’?
A) 1.9%
B) 3.7%
C) 7.5%
D) 14.6%
E) Cannot be calculated without the standard deviation of the
distribution.
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PERDI – Version 2
I – 20 – Version 2
The wait to get through a bridge’s toll booth complex at rush hour is 3
minutes, 45 seconds with a standard deviation of 58 seconds. What is
the probability that the next 25 cars in line have to wait on average more
than 4 minutes? Assume normality of waiting times.
A) .098
B) .398
C) .406
D) .496
E) No conclusion can be made.
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PERDI – Version 2
I – 21 – Version 2
The analysis of a random sample of 1,000 diners at the chain InFront
Steakhouse with many restaurants throughout the country indicates that
a 95% confidence interval for the mean percent tip is (14.23%, 18.79%).
Could this information be used to conduct a hypothesis test at the 5%
level that people tip at least 18% at this restaurant?
A) No, because the value of " is not known.
B) No, because there is no information whether the tips are normally
distributed.
!
C) Yes, because the 95% confidence interval contains numbers beyond
18%, we would reject the null hypothesis and conclude that there is
enough evidence to suggest that the average tip is at least 18%.
D) Yes, because 18% is in the 95% confidence interval, we would fail to
reject the null hypothesis and conclude that there isn’t enough
evidence to suggest that the average tip is at least 18%.
E) Yes, because 18% is in the 95% confidence interval, we would reject
the null hypothesis and conclude that there is enough evidence to
suggest that the average tip is at least 18%.
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PERDI – Version 2
!
I – 22 – Version 2
A particular camera that is available over the Internet is sold at a variety
of prices. We are interested in the average price of all sites that sell it on
the Internet. A simple random sample of sites was taken and produced a
sample mean x of $250. A 95% confidence interval for the population
mean price is $250 ± $17.50. Which of the following statements are
true?
!
A) If!100 samples were taken and the average price calculated, 95 of
these averages would be between $232.50 and $267.50.
B) If the true population average µ is $270, then x of $250 would be
highly unlikely.
C) P($232.50 < x < $267.50) = 0.95.
!
!
D) P($232.50 < µ < $267.50) = 0.95.
E) 95% of the population prices fall between $232.50 and $267.50.
!
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PERDI – Version 2
I – 23 – Version 2
A radio-sports show host predicted that he was 95% certain that if
Philadelphia sports fans were to rank their teams in order of favorites, it
would be:
Eagles: 45%
Phillies: 30%
Flyers: 15%
76ers: 10%
In a random sample of callers over a month period, the talk show host
found that the favorite teams were the numbers in the table below.
Ignoring the possible objections of the way the poll was taken, what
would be the correct conclusion that he should make regarding his
prediction above?
Eagles
57
A)
B)
C)
D)
E)
Phillies
57
Flyers
18
76ers
11
His predictions are wrong.
His predictions are right.
There is not enough evidence that he is wrong.
There is not enough evidence that he is right.
His predictions about the Eagles and Phillies were wrong.
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PERDI – Version 2
I – 24 – Version 2
When filling a large soda cup (64 ounces), a particular brand of machine
has a known standard deviation of .45 ounces. A researcher wants to
know how many sample cups of soda he must fill to have a margin of
error less than .1 ounces with 95% confidence.
However, the machine’s manager wants to be surer so he asks for 98%
confidence. How many more samples must the researcher take to go
from 95% confidence to 98% confidence?
A) 1
B) 2
C) 9
D) 22
E) 32
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PERDI – Version 2