Download AP Statistics - Fall Final Exam

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AP Statistics Final Exam - Fall 2014
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. If a distribution is skewed to the right, which of the following is true?
a. The mean must be less than the median.
b. The mean and median must be equal.
c. The mean must be greater than the median.
d. The mean is either equal to or less than the median,
e. It’s impossible to tell which of the above statements is true without seeing the
data.
____
2. Rainwater was collected in water collectors at 30 different sites near an industrial complex and the
amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following
stemplot of the data was constructed.
Which of the following boxplots is a correct representation of the same distribution?
a.
b.
c.
d.
e.
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AP STATISTICS FALL FINAL EXAM - 2014
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3. A small company that prints custom t-shirts has 6 employees, one of whom is the owner and
manager. Suppose the owner makes $120,000 per year and the other employees make between
$40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which
of the following describes how the company’s mean and median salaries would change?
a. The mean and median would both increase by $5,000.
b. The mean would increase by $5,000 and the median would not change.
c. The mean would increase by $6,000 and the median would not change.
d. The median would increase by $6,000 and the mean would not change.
e. The mean would increase by $6,000, but we cannot determine the change in the
median without more information.
____
4. A medical researcher collects health data on many women in each of several countries. One of the
variables measured for each woman in the study is her weight in pounds. The following list gives
the five-number summary for the weights of adult women in one of the countries.
Country A:
92, 110, 120, 160, 240
About what percent of Country A women weigh between 110 and 240 pounds?
a.
b.
c.
d.
e.
50%
65%
75%
85%
95%
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AP STATISTICS FALL FINAL EXAM - 2014
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The population of the United States is aging, though less rapidly than in other developed countries.
At right is a stemplot of the percentages of residents aged 65 and older in each of the 50 states,
according to the 2010 census.
____
5. There are three outliers: Alaska has the lowest percentage of older residents, Utah had the second
lowest, and Florida has the highest. What is the percentage for Utah?
a.
b.
c.
d.
e.
7.7%
9.0%
14.0%
15.0%
90%
____
6. The Interquartile range for the distribution of 50 states according to the 2010 census is:
a. 12.4% to 14.3%
b. 12.4% to 14.5%
c. 1.8%
d. 1.9%
e. 2.1%
____
7. A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just
been discovered that the maximum value in the distribution, which was erroneously recorded as 40,
actually had a value of 50. If we make this correction to the data, then
a. the mean remains the same, but the median is increased.
b. the mean and median remain the same.
c. the median remains the same, but the mean is increased.
d. the mean and median are both increased.
e. we do not know how the mean and median are affected without further
calculations, but the variance is increased.
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AP STATISTICS FALL FINAL EXAM - 2014
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A
8. The heights (in centimeters) of the male and female students in a class are summarized in the
following boxplots:
Which of the following is conclusions can be drawn from this graph?
a. About 50% of the male students have heights between 170 and 178 centimeters.
b. About 25% of the male students are taller than the tallest female student.
c. The median height of male students is about 163 centimeters.
d. The mean height of male students is about 178 centimeters.
e. For female students, the mean height is lower than the median height.
____
9. The area under the standard Normal curve corresponding to –0.3 < Z < 1.6 is
a. 0.3273
b. 0.4713
c. 0.5631
d. 0.9542
e. none of the above
____ 10. Which of the following properties is true for all Normal density curves?
I.
II.
III.
a.
b.
c.
d.
e.
They are symmetric.
The curve reaches its peak at the mean.
95% percent of the area under the curve is within one standard
deviation of the mean.
I only
II only
I and II only
I and III only
All three statements are correct.
Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a
Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce.
____ 11. The percent of bags that will contain between 16.0 and 16.1 ounces is about
a. 10
b. 16
c. 34
d. 68
e. None of the above
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____ 12. The distribution of the heights of students in a large class is roughly Normal. Moreover, the average
height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the
standard deviation of the height distribution is approximately equal to
a.
b.
c.
d.
e.
2
3
6
9
12
____ 13. If your score on a test is at the 60th percentile, you know that your score lies
a. below the first quartile.
b. between the first quartile and the median.
c. between the median and the third quartile.
d. above the third quartile.
e. There is not enough information to say where it lies relative to the quartiles.
For children between the ages of 18 months and 29 months, there is an approximately linear
relationship between height and age. The relationship can be represented by
y8= 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months).
____ 14. Joseph is 22.5 months old. What is his predicted height?
a. 50.80
b. 64.96
c. 65.96
d. 79.11
e. 87.40
____ 15. Loretta is 20 months old and is 80 centimeters tall. What is her residual?
a. -2.47
b. 2.47
c. -12.60
d. 12.60
e. 77.53
____ 16. Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals
shows a curved pattern?
a. A straight line is not a good model for the data.
b. The correlation must be 0.
c. The correlation must be positive
d. Outliers must be present
e. The regression line might or might not be a good model for the data, depending
on the extent of the curve.
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Scenario 3-9
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of
natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The
house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is
y8 = 1344  19x
____ 17. Use Scenario 3-9. When the temperature goes up 1 degree, what happens to the gas usage predicted by the
regression line?
a. It goes up 1 cubic foot.
b. It goes down 1 cubic foot.
c. It goes up 19 cubic feet.
d. It goes down 19 cubic feet.
e. Can't tell without seeing the data.
____ 18. Use Scenario 3-9. What does the number 1344 represent in the equation?
a. Predicted gas usage (in cubic feet) when the temperature is 19 degrees Fahrenheit.
b. Predicted gas usage (in cubic feet) when the temperature is 0 degrees Fahrenheit.
c. It’s the y-intercept of the regression line, but it has no practical purpose in the context of
the problem.
d. The maximum possible gas a household can use.
e. None of the above.
____ 19. A researcher for a consumer products company is field testing a new formula for laundry detergent.
He has contracted with 60 families, each with two children, who have agreed to test the product. He
randomly assigns 30 families to the group that will use the new formula and 30 to the group that will
use the company’s current detergent formula. The most important reason for this random
assignment is that
a. randomization makes the analysis easier since the data can be collected and
entered into the computer in any order.
b. randomization eliminates the impact of any confounding variables.
c. randomization is a good way to create two groups of 30 families that are as
similar as possible, so that comparisons can be made between the two groups.
d. randomization ensures that the study is double-blind.
e. randomization reduces the impact of outliers.
____ 20. The following numbers appear in a table of random digits:
38683 50279 38224 09844 13578 28251 12708 24684
A scientist will be measuring the total amount of leaf litter in a random sample (n = 5) of forest sites
selected without replacement from a population of 45 sites. The sites are labeled 01, 02, . . . , 45 and
she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which
of the following is correct?
a. Her sample is 38, 25, 02, 38, 22
b. Her sample is 38, 68, 35, 02, 22
c. Her sample is 38, 35, 27, 28, 08
d. Her sample is 38, 65, 35, 02, 79
e. Her sample is 38, 35, 02, 22, 40
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AP STATISTICS FALL FINAL EXAM - 2014
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____ 21. A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000
undergraduate students and a separate SRS of 100 of the 5,000 graduate students. What is the term
for this kind of sample?
a. Simple random sample.
b. Simple random sample with blocking.
c. Multistage random sample.
d. Stratified random sample.
e. Cluster sample.
The two-way table below gives information on seniors and juniors at a high school and by which
means they typically get to school.
Car
Bus
Walk Totals
Juniors
146
106
48
300
Seniors
146
64
40
250
Totals
292
170
88
550
____ 22. You select one student from this group at random. What is the probability that this student typically
takes a bus to school?
a.
b.
c.
d.
e.
0.256
0.309
0.353
0.455
0.604
____ 23. You select one student from this group at random. If the student says he is a junior, what is the
probability that he walks to school?
a.
b.
c.
d.
e.
0.073
0.160
0.455
0.600
0.833
____ 24. You play tennis regularly with a friend, and from past experience, you believe that the outcome of
each match is independent. For any given match you have a probability of 0.6 of winning. The
probability that you win the next two matches is
a. 0.16.
b. 0.36.
c. 0.4.
d. 0.6.
e. 1.2.
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AP STATISTICS FALL FINAL EXAM - 2014
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____ 25. There are 10 red marbles and 8 green marbles in a jar. If you take three marbles from the jar
(without replacement), the probability that they are all red is:
a. 0.069
b. 0.088
c. 0.147
d. 0.444
e. 0.171
____ 26.A marketing survey compiled data on the total number of televisions in households. If X = the number
of televisions in a randomly-selected household, and we omit the rare cases of more than 5
televisions, then X has the following distribution:
0
1
2
3
4
5
X
0.24 0.37 0.20 0.11 0.05 0.03
P(X)
What is the probability that a randomly chosen household has at least two televisions?
a.
b.
c.
d.
e.
0.19
0.20
0.29
0.39
0.61
____ 27. Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given
by
a.
b.
c.
d.
e.
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AP STATISTICS FALL FINAL EXAM - 2014
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____ 28. Which of the following random variables is geometric?
a. The number of phone calls received in a one-hour period
b. The number of times I have to roll a six-sided die to get two 5s.
c. The number of digits I will read beginning at a randomly selected starting point in
d.
e.
a table of random digits until I find a 7.
The number of 7s in a row of 40 random digits.
All four of the above are geometric random variables.
____ 29. According to the DuPont 2012 Global Automotive Color Popularity Report, 23% of all cars
manufactured in 2012 were white. In a random sample of 100 cars parked in long-term parking at
Philadelphia International Airport, 19% of the cars were white. Which of the following statements
is true?
a. 19% and 23% are parameters, 100 is a statistic.
b. 23% is a parameter, 19% is a statistic.
c. 23% is a statistic, 19% is a parameter.
d. 19% and 23% are statistics, 100 is neither a parameter nor a statistic.
e. 19%, 23%, and 100 are all statistics.
____ 30. In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200
adults are randomly selected for a market research campaign. The sampling distribution of the
sample mean IQ is
a. exactly Normal, mean 112, standard deviation 20.
b. approximately Normal, mean 112, standard deviation 0.1.
c. approximately Normal, mean 112, standard deviation 1.414.
d. approximately Normal, mean 112, standard deviation 20.
e. exactly Normal, mean 112, standard deviation 1.414.
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AP STATISTICS FALL FINAL EXAM - 2014
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Free Response
1. The states differ greatly in the kinds of severe weather that afflict them. The histogram below shows the
distribution of average annual property damage caused by tornadoes over the period from 1950 to 1999 in the
50 United States. (To adjust for the changing buying power of the dollar over time, all damages were restated
in 1999 dollars.)
(a) Describe the important features of this distribution.
(b) When asked for summary statistics, MINITAB produced the following output:
Variable N Mean
Damage 50 22.39
SE Mean StDev Minimum Q1 Median Q3 Maximum
3.60
25.45 0.00
2.23 12.66 41.63 88.60
The histogram suggests that there may be outliers on the high end. Use the 1.5 x IQR rule of thumb to show
that no values in this distribution meet this criterion for outliers.
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AP STATISTICS FALL FINAL EXAM - 2014
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2. Below are the lengths, in minutes, of the 25 most popular movies, as voted on by visitors to a web site
devoted to movies.
142
195
201
139
106
175
96
121
130
109
200
133
102
178
165
161
124
146
115
118
154
152
207
112
136
(a) Make a stemplot of these data. Describe the distribution.
(b) The longest movie on the list, at 207 minutes, is Akira Kurosawa’s classic The Seven Samurai. Suppose
its place on the list was replaced by Andy Warhol’s Sleep, which is 321 minutes of a man sleeping. Without
performing any calculations, indicate whether each of the following measures of center and spread would
increase, decrease, or remain the same.




mean
median
standard deviation
interquartile range
3. A local post office weighs outgoing mail and finds that the weights of first-class letters is
approximately Normally distributed with a mean of 0.69 ounces and a standard deviation of 0.16
ounces.
(a) First-class letters weighing more than 1 ounce require additional postage. What proportion of
first-class letters at this post office require additional postage?
(b) What is the 60th percentile of first-class letter weights?
4. Read the following brief article about aspirin and alcohol.
(a) Explain why this is an experiment and not an observational study.
(b) Identify the explanatory and response variables.
(c) Identify the experimental design used in this study. Justify your answer.
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AP STATISTICS FALL FINAL EXAM - 2014
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5. Meadowbrook School surveys the families of its students and determines the following: if a family is chosen
at random, the probability that they own a dog is 0.38, the probability they own a cat is 0.23, and the
probability they own both a dog and a cat is 0.12.
(a) Let D = randomly-chosen family owns a dog, and C = randomly-chosen family owns a cat. Sketch a
Venn diagram or two-way table that summarizes the probabilities above.
Find each of the following.
(b) The probability that a randomly-selected family owns a dog or a cat.
(c) The probability that a randomly-selected family does not own either pet.
(d) The probability that a randomly-selected family dog owner also owns a cat.
6. Witney Pete, a professional dart player, has a 70% chance of hitting the bull’s eye on a dartboard
with any throw. Assume that each throw of a dart is independent.
(a) Suppose Pete throws darts until he hits his first bull’s eye. Find the probability that his first
bull’s eye occurs on the third throw.
(b) What is the probability that Pete hits exactly 8 of his next 10 shots?
(c) What is the probability that Pete hits 5 or fewer of his next 10 shots?
7. Below is some data on the relationship between the price of a certain manufacturer’s flat-panel LCD
televisions and the area of the screen. We would like to use these data to predict the price of
televisions based on size.
Screen Area (sq. in)
Price (Dollars)
154
250
207
265
289
330
437
375
584
575
683
650
(a) Use your calculator to find the equation of the least-squares regression equation. Write the
equation below, defining any variables you use.
(b) This manufacturer also produces a television with a screen size of 943 square inches. Would it
be reasonable to use this equation to predict the price of that television? Explain.
(c) Calculate the residual for the television that has a screen area of 437 square inches.
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ID: A
AP Statistics Final Exam - Fall 2014
Answer Section
MULTIPLE CHOICE
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2.
3.
4.
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6.
7.
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30.
ANS:
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C
B
B
C
B
D
C
B
C
C
C
B
C
D
B
A
D
B
C
E
D
B
B
B
C
D
B
C
B
C
PTS:
PTS:
PTS:
PTS:
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
TOP: Interpret slope
TOP: Interpret y-intercept
1
ID: A
OTHER
1. ANS:
(a) The distribution of damages ranges from near $0 to near $90 million and is strongly skewed to the right.
This suggests that many states suffered very little damage, but a small number of states suffered a great deal
of damage.
(b) Min. = 0 Q1 = 2.23 Med. = 12.66 Q3 = 41.63 Max. = 88.6. The distance from the median to Q3 is
much greater than the distance from the median to Q1, and the distance from Q3 to the maximum is much
greater than the distance from Q1 to the minimum. Both of these comparisons suggest that the distribution is
skewed right.
(c) IQR = 41.63 – 2.23 = 39.40; 1.5 x IQR = 59.10. Q1 – 59.10 < 0 so there are no low outliers, and Q3 +
59.10 = 100.73, so there are no high outliers.
PTS: 1
2. ANS:
(a) Stemplot shown below. (b) Remember your SOCS: Shape - skewed right; Outliers - 195, 200, 201 and 207
are slight outliers; Center - the median (middle number) is 139 minutes; Spread - from 96 minutes to 207
minutes. (c) Mean and standard deviation will increase, median and interquartile range will not change.
PTS: 1
3. ANS:
(a) z= (1-0.69)/0.16 = 1.94, which has a proportion of 1 – 0.9738 = .0262 letters above it requiring
additional postage.
(b) z for 60th percentile is 0.25, and 0.69 _0.25(0.16) = 0.73 ounces.
PTS: 1
2
ID: A
4. ANS:
(a) This is an experiment because treatments (aspirin and alcohol; alcohol only) are imposed on the
subjects.
(b) Explanatory variable: Aspirin consumption; Response: blood alcohol content.
(c) Matched pairs experiment. Each subject was given both treatments (aspirin before drinking and
no aspirin) and thus acted as his own “pair.”
PTS: 1
5. ANS:
a. Venn diagram
.
b. P(D  C) = .26 + .12 + .11 = .49
c. P(DC  CC) = 0.51
d. P(C | D) = .12 / (.26 + .12) = .12 / .38 = .316
PTS: 1
6. ANS:
a. Geometric probability: (0.3) 2 (0.7)  0.063
10!
(.7) 8 (.3) 2  binompdf(10,0.7,8)  0.2335
8!2!
c. Binomial Cumulative Probability: P ( X  5)  binomcdf(10,0.7,5)  0.1503
b. Binomial Probability: P ( X  5) 
PTS: 1
7. ANS:
a. y8  105.74  0.769x; y8 = predicted price, x = screen area.
b. 943 sq. in. is well beyond the range of screen areas used to produce the regression line, so this
would be extrapolation. We cannot be sure that the relationship described by this line holds outside
the range of available data.
c. y  y8  375  (105.74  0.769(437))  375  441.47  66.79 . Since the residual is negative, the
observed value is lower than the value predicted by the regression. This suggests that this particular
television is a good buy!
PTS: 1
3