Practice Set 13 – Data Inferences
Calculator Required
Objectives
 Create and interpret a confidence interval
 Understand the effect that the confidence level and sample size has on the margin of error
 Find the margin of error and sample statistic given a confidence interval
Notes







Confidence Interval
Confidence Level
Margin of Error
Population
Population Parameter
Sample
Sample Statistic
1. (ACT/SAT) Standard movie projectors project 24 still images, known as frames, each second. If a certain
movie uses the standard frame rate and has exactly 129,600 total frames, then, to the nearest minute, how
long is the movie?
2. (ACT/SAT) Multiple choice – Based upon the table below, which basketball player has the greatest assist to
turnover ratio?
Player
Assists
Turnovers
A
246
90
B
C
D
A. Player A
B. Player B
93
135
252
32
38
82
C. Player C
D. Player D
3. (ACT/SAT) Multiple choice - The table below summarizes the results of a survey given in 2014 to 8,000
randomly selected undergraduates at a university regarding what they use as their primary computer.
Computing Device Preference in University Students
1st Year
2nd Year
3rd Year
4th Year
Total
Students
Students
Students
Students
Tablet
879
590
903
280
2652
Laptop
549
894
1146
310
4190
Desktop
445
614
842
548
2449
Total
1783
2098
2891
1134
8000
According to the survey, which of the following statements are true?
I. The approximate relative frequency that a student in the survey uses a tablet for their primary computer is
33%.
II. The fraction of 1st year students that use tablets as their primary computer is less than the fraction of 3 rd
year students that use tablets for their primary computer.
1
III. About
of those students that reported using a desktop as their primary computer were 3 rd year
3
students.
A. I only
B. I and II only
Problem Solving and Data Analysis
C. I and III only
D. II and III only
75
4. (ACT/SAT) Multiple choice – A sociologist conducts a survey investigating the use of mobile devices to
access different types of content in Brazil. The incomplete table below shows the relative frequencies of
different age groups that use their mobile devices to read media, watch TV and movies, both read media and
watch TV/movies, or neither.
Use of Mobile Devices to Access Content by Age Group
15 to 24
25 to 65
Only Read Media
12%
37%
Only Watch TV/Movies
16%
9%
Both
64%
-Neither
8%
11%
175 of the people surveyed were 15 to 24 and the other 300 people surveyed were 25 to 65. What is the
probability that people who use their mobile devices to both read media and watch TV/movies are ages 25 to
65?
A. 28%
B. 36%
C. 43%
D. 54%
5. (ACT/SAT) Multiple choice – The graph below in the RI-plane shows the current, I, in amperes for a circuit
with a resistor having R ohms of resistance.
What is the significance of the value I = 4 shown by the dotted line?
A.
B.
C.
D.
The current for a resistor with 0 ohms of resistance is 4 amperes.
The current reaches a minimum when the resistor has a resistance of 4 ohms.
As the current becomes large the resistance becomes approximately 4 ohms.
As the resistance becomes large, the current becomes approximately 4 amperes.
6. (ACT/SAT) Multiple choice – An ink printer sprays droplets of ink onto a piece of paper to form text. An
electric potential of p millivolts (mV) is used to control the horizontal impact distance, h, measured in
micrometers  m  from the target where positive or negative values of h represent distances to the right or
left of the target respectively. Without an electric potential, 0 mV would be created and the droplet would
impact 100 m to the left of the target. An electric potential producing 200 mV allows the droplet to impact
the target exactly. Which of the following graphs in the ph-plane could represent this situation?
A.
76
B.
C.
D.
Problem Solving and Data Analysis
Problems 7 and 8 use the following scenario:
In a poll of 1,578 randomly selected American adults, 44.8% of the respondents said that airlines should allow in
flight calls on airplanes. The poll reported a margin of error of 2.5% at a 95% confidence level.
7. Create the 95% confidence interval for the percent of American adults who believe airlines should allow in
flight calls on airplanes.
8. Which of the following is most likely to be equal to the percentage of all American adults who say that airlines
should allow in-flight calls?
A. 40%
B. 43%
C. 48%
D. 95%
Problems 9 and 10 use the following scenario:
A random sample of 35 four-door passenger vehicles had a mean gas mileage, in miles per gallon (mpg), of 25.9
mpg. The estimate had a margin of error of 2.6 mpg at a 98% confidence level.
9. Create the 98% confidence interval for the mean gas mileage of all four-door passenger vehicles.
10. Select All That Apply – Of the following, which is a plausible value for the true mean gas mileage of all fourdoor passenger vehicles?
A. 23 mpg
B. 24 mpg
C. 28 mpg
D. 30 mpg
Problems 11 and 12 use the following scenario:
A random sample of international flights in 2013 showed that 79% of the flights arrived within 15 minutes of their
scheduled arrival time, and this estimate had a margin of error of 3% at a 95% confidence level.
11. Which of the following conclusions is best?
A.
B.
C.
D.
Exactly 79% arrived within 15 minutes of their scheduled times.
Exactly 76% arrived within 15 minutes of their scheduled times.
Between 76% and 82% arrived within 15 minutes of their scheduled times.
Between 92% and 98% arrived within 15 minutes of their scheduled times.
12. In 2012, 75% of international flights arrived within 15 minutes of their scheduled arrival time. Does this
sample provide evidence that this percentage is higher in 2013 than in 2012? Explain your reasoning.
Problems 13 and 14 use the following scenario:
In a poll of 14,607 randomly selected adults in the United States, those polled spent an average of $95 per day in
November of last year, as compared with $91 per day in November two years ago. The estimates had a margin
of error of $4 at the 95% confidence level.
13. Create the 95% confidence interval for the average amount of money a US adult spends per day in
November.
14. Which of the following is a reasonable claim to make based on this sample?
A. All adults in the United States spent between $91 and $99 daily last November.
B. 95% of adults in the United States spent between $91 and $99 daily last November.
C. It is plausible that average daily spending of adults in the United States remained the same in November of
last year as it was in November two years ago.
D. Between 91% and 99% of adults in the United States spent $4 more daily last November than in November
two years ago.
Problem Solving and Data Analysis
77
Problems 15 and 16 use the following scenario:
After randomly sampling 1,000 cars, a car wash determined with 95% confidence that the mean time needed to
wash a car is 8 minutes and 56 seconds with a margin of error of 7 seconds.
15. Which of the following could be the bounds of a 90% confidence interval based on the same sample?
A.
B.
C.
D.
from 8 minutes and 50 seconds to 9 minutes and 5 seconds
from 8 minutes and 40 seconds to 9 minutes
from 8 minutes and 40 seconds to 9 minutes and 5 seconds
from 8 minutes and 50 seconds to 9 minutes and 3 seconds
16. A customer complains after waiting for exactly 9 minutes at the car wash. Is it unreasonable for the car wash
to take exactly 9 minutes? Justify your answer.
Problems 17 – 21 use the following scenario:
In a particular county, a sample of 1,500 of the 50,000 households showed that 84% of the households lived in
the same residence as they had the previous year. The estimate had a margin of error of 1.5% at the 90%
confidence level.
17. Based on this information, which statement about all households in the county is most appropriate?
A. Exactly 42,000 of all households in the county lived in the same residence as the previous year.
B. Exactly 42,000 of all households in the county thought their landscaping was too cute to move away from and
stayed in the same residence as the previous year.
C. Approximately 42,000 of all households in the county lived in the same residence as the previous year.
D. Approximately 42,000 of all households decided against changing their residence from the previous year
because moving is too much of a pain.
18. How would the margin of error be affected if the sample size was increased?
A. It would increase
B. It would stay the same
C. It would decrease
D. Impossible to determine
19. How would the margin of error be affected if the sample size was decreased?
A. It would increase
B. It would stay the same
C. It would decrease
D. Impossible to determine
20. How would the margin of error be affected if the confidence level was increased?
A. It would increase
B. It would stay the same
C. It would decrease
D. Impossible to determine
21. How would the margin of error be affected if the confidence level was decreased?
A. It would increase
78
B. It would stay the same
C. It would decrease
D. Impossible to determine
Problem Solving and Data Analysis
22. In the National Health and Nutrition Examination Survey, 80.5% of the participants had healthy levels of highdensity lipoprotein (HDL) cholesterol, the estimate has a margin of error of 1.5% at a confidence level of 95%.
The participants were a random sample of the United States (US) residents. The US population at the time of the
study was 316 million people, and the estimate at a 95% confidence level of the number of people in the US who
had healthy levels of HDL cholesterol was reported.
Select all that Apply - Which of the following changes to the study would results in a smaller margin of error?
A.
B.
C.
D.
Increase the sample size
Decrease the sample size
Increase the confidence level
Decrease the confidence level
23. Select all that Apply - In a poll of 1,578 randomly selected American adults, 44.8% of the respondents said
that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of 2.5% at a 95%
confidence level. Which of the following is could possibly be equal to the percentage of all American adults who
say that airlines should allow in-flight calls?
A. 42%
B. 43%
C. 44%
D. 46%
E. 47%
Problems 24 and 25 use the following scenario:
A random sample of 35 four-door passenger vehicles reported that the mean gas mileage, in miles per gallon
(mpg), at the 95% confidence level is between 22.7 and 29.1 mpg.
24. What is the value of the sample statistic?
25. What is the value of the margin of error of the confidence interval?
Problems 26 and 27 use the following scenario:
A random sample of international flights in 2018 was used to determine the number of flights that arrive within 15
minutes of the scheduled arrival time. The researchers reported at the 95% confidence level that between 77.9%
and 84.1% of all international flights should arrive within 15 minutes of the scheduled time.
26. What is the value of the sample statistic?
27. What is the value of the margin of error?
Problem Solving and Data Analysis
79
Practice Set 14 – Median, Mean, and Range
Calculator Required
Objectives
 Calculator the mean, median, and range from various representations of data
 Analyze the effects changing a data will have on the mean and median
Notes



Mean
Median
Range
1. (ACT/SAT) An architect is creating a scale model of a building with a rectangular base. The ratio of the
building’s base length to the scale model’s base length is 110 in : 3 in. If the length of the base of the scale
model is 9 inches (in), what is the length of the base of the building to the nearest foot?
2. (ACT/SAT) Multiple choice – Strain is the ratio of change in length to the original length. Based on the
lengths, in millimeters (mm), in the table below, which wire experienced the greatest strain?
Wire
Wire 1
Wire 2
Wire 3
A. Wire 1
C. Wire 3
Original length (mm)
6
8
11
New length (mm)
8
10
14
B. Wire 2
D. Wires 1 and 2 had the same strain.
3. (ACT/SAT) Multiple choice - The relative frequencies of US stores offering paper and or plastic bags to their
custom are tabulated in the table below.
Paper and Plastic Bag Options in US Stores
Type of Store
Paper Only
Plastic Only
Both
Neither
Total
Supermarkets
3%1%
3%
27%
1%
34%
Convenient Stores
2%
11%
3%
1%
17%
Department Stores
16%
4%
2%
0%
22%
Clothing Stores
9%
5%
1%
0%
15%
Other Stores
4%
4%
3%
1%
12%
Total
34%
27%
36%
3%
100%
A total of 2,200 randomly selected stores nationwide were included in creating this table. According to the
data, what is the approximate probability that a store that offers neither paper nor plastic bags is a
supermarket?
A.
80
1
100
B.
1
34
C.
3
34
D.
1
3
Problem Solving and Data Analysis
4. (ACT/SAT) Multiple choice – A holistic veterinarian conducts a study of the use of slippery elm to treat
gastrointestinal symptoms in dogs. The following incomplete table shows the number of positive and negative
outcomes associated with the prescription of this medication within two days.
Positive Outcomes of Medication by Weight
Positive Outcomes
Negative Outcomes
Larger than 50 pounds
137
39
29.1 to 50 pounds
312
-14.1 to 29 pounds
236
-6 to 14 pounds
-115
Overall, the prescription of this medication showed positive outcomes within two days for approximately 80%
of all dogs in this study. This result was consistent for dogs in each weight category. Based on the
information provided, approximately what percentage of dogs in this study were larger than 50 pounds?
A. 12%
B. 18%
C. 21%
D. 39%
5. (ACT/SAT) Multiple choice - An insurance plan pays a portion of the total cost incurred by a participant. The
graph below in the CI-plane shows the amount paid by insurance, I, for any given total cost incurred by a
member, C, both in dollars.
What is the best interpretation of the average rate of change between the point (C, I) = (400, 0) and
(C, I) = (2,800, 1,800) indicated on the graph?
A. If the total cost is between 400 and 2,800 dollars, then insurance will pay about 75 percent of the total
cost.
B. If the total cost is between 400 and 2,800 dollars, then insurance will pay about 25 percent of the total
cost.
C. For each dollar of the total cost above 400 and below 2,800, insurance pays about 75 cents.
D. For each dollar of the total cost above 400 and below 2,800, insurance pays about 25 cents.
6. (ACT/SAT) Multiple choice – Amber has an interest-earning account which allows her to withdraw and
deposit funds at any time. The amount, A, in thousands of dollars t years after opening the account is
graphed in the tA-plane. Amber performs a withdrawal 2 years after opening the account, immediately
decreasing the amount. She performs a deposit 4 years after opening the account, immediately increasing
the amount to equal the amount just before the withdrawal. At all other times, the amount is increasing.
Which of the following graphs could represent her account?
A.
B.
Problem Solving and Data Analysis
C.
D.
81
Problems 7 – 9 use the following scenario:
A linguistics library contains several archives of language samples. The table below gives the number of distinct
languages referenced in each archive.
Archive
Number of distinct
languages
Archive A
Archive B
Archive C
Archive D
Archive E
Archive F
Archive G
111
3
136
26
53
258
17
7. What is the mean of numbers of distinct languages referenced?
8. What is the median of numbers of distinct languages referenced?
9. What is the range of numbers of distinct languages referenced?
Problems 10 – 12 use the following scenario:
The price of a ticket to a concert varies depending on the day of the week, as shown in the table below.
Day
Ticket Price
Monday
$56
Tuesday
$45
Wednesday
$45
Thursday
$73
Friday
$73
Saturday
$73
Sunday
$56
10. What is the mean of ticket price in dollars, to the nearest cent?
11. What is the median of ticket prices in dollars?
12. What is the range of ticket prices in dollars?
Problems 13 – 15 use the following scenario:
The length of the land boundary (in thousands of kilometers) of each country in South America is shown below.
Each value is rounded to the nearest thousand kilometers.
13. What is the mean length of land boundary lengths, in thousands of kilometers? Round your answer to the
nearest thousandth.
14. What is the median length of land boundary lengths, in thousands of kilometers?
15. What is the range of lengths of land boundary lengths, in thousands of kilometers?
82
Problem Solving and Data Analysis
 bbl 
16. For each country in East Asia, the average number of barrels of crude oil exported per day 
 is plotted
 day 
bbl
.
below to the nearest 30
day
Which of the following statements about the distribution of the data is true?
A. It is most likely that an East Asian country’s exports are less than 30
bbl
.
day
B. It is most likely that an East Asian country’s exports are greater than 30
bbl
.
day
bbl
bbl
.
than greater than 30
day
day
D. The data does not give enough information to predict the likelihood of an East Asian country’s exports being
bbl
.
more or less than 30
day
C. It is equally likely that an East Asian country’s exports are less than 30
17. Data was taken on carpooling in Tallahassee, Florida. For each person’s daily commute, the number of
people in the car was recorded. The results are summarized in the bar graph below.
What is the median number of people in the car?
18. The table below partially reports the numbers of civil aircraft produced in the United States during the course
of 5 months.
Month
A
B
C
D
E
Civil aircraft produced
400
?
286
350
290
If there was a mean of 325 civil aircraft produced during that time, how many were produced in month B?
Problem Solving and Data Analysis
83
19. The table below partially summarizes the percent of residents in different counties who participate in
performing arts at least once a month. The percentages have a range of 12.9%.
County
Percentage
A
9.8%
B
8.8%
C
7.8%
D
5.2%
E
17.3%
F
4.7%
G
?
H
4.7%
What could be the percentage of county G residents who participate in performing arts at least once a month?
Problems 20 and 21 use the following scenario:
A golfer measured the speed, in miles per hour (mph) of several drives with the same golf club. The frequency
table below tells how often each speed occurred.
Speed (mph)
Frequency
117
1
119
3
120
1
121
4
123
1
125
2
126
1
127
6
20. What is the mean speed of the drives? Round to the nearest hundredth.
21. What is the median speed of the drives?
Problems 22 and 23 use the following scenario:
On a message board, participants listed words whose letters are all in alphabetical order, such as “almost.” The
table below lists the number of words they listed with each letter count.
Letter Count
Number of words listed
4 letters
12
5 letters
49
6 letters
12
7 letters
9
8 letters
1
22. What was the median letter count of the words they listed?
23. What is the mean letter count of the words they listed? Round to the nearest hundredth.
24. A candidate in a local election analyzed the voter data for 7 of the towns where she was on the ballot. If the
median number of votes that she received from the 7 towns was 421, then which statement must be true
about this election?
A.
B.
C.
D.
84
The total number of votes the candidate received in all 7 towns was 2947.
The total number of votes the candidate received in each of the 7 towns was 60.
The candidate received at least 421 votes in at least 4 of the 7 towns.
The candidate received exactly 421 votes in 2 of the 7 towns.
Problem Solving and Data Analysis
25. The dot plot below depicts the number of home runs hit by members of the San Francisco Giants during the
2014 baseball season.
If the player who hit the most home runs was removed from the data set, how would the mean of the data set be
affected?
A.
B.
C.
D.
It would increase.
It would decrease.
It would remain the same.
There is not enough information to determine the impact on the mean number of home runs.
26. The number of bedrooms in each house in New Mexico is recorded and shown in the bar graph below.
The rightmost category combines all houses with at least 5 bedrooms in it. According to the bar graph, what can
we say about the mean number of bedrooms in New Mexico houses?
A.
B.
C.
D.
The mean is less than 3.
The mean is greater than 3.
The mean is equal to 3.
There is not enough information to compare the mean to 3.
 kg 
27. A farmer recorded the total fresh yield, in kilograms per hectare   , of several varieties of onion crops.
 ha 
The table below gives the results.
Crop
A
B
C
D
E
 kg 
Yield  
 ha 
46,400
75,000
75,930
53,130
42,530
If the farmer tried a new variety, with a 57,930
kg
yield, how would it affect the median and mean of the crop
ha
yields?
A.
B.
C.
D.
Both the median and the mean will increase.
Both the median and the mean will decrease.
The median will decrease, but the mean will increase.
The median will increase, but the mean will decrease.
Problem Solving and Data Analysis
85
Practice Set 15 – Boxplots and Histograms
Calculator Required
Objectives
 Create and interpret boxplots
 Interpret histograms
 Discuss how changing a data set affects the visual representation of the data set
Notes








Boxplot
Five-Number Summary
Interquartile Range
Outlier
Quartile
Histogram
Bin
Inclusive/Exclusive
1. (ACT/SAT) 3.01-3.11 Following a lightning strike, thunder travels at a speed of 1127 feet per second. Using
her stopwatch, Fatima counts 4 seconds after a lightning strike before she hears thunder. To the nearest
tenth of a mile, how many miles from the lightning strike is Fatima? (1 mile = 5280 feet)
2. (ACT/SAT) Multiple choice – The musical interval between two sounds is called an “octave” if the ratio of the
sounds’ frequencies is 2 : 1. The table below shows the names of the musical intervals between two sounds
based on the ratios of the two sounds’ frequencies.
Name of the musical interval
Major third
Perfect fourth
Perfect fifth
Ratio of two sound frequencies
4:5
3:4
2:3
Major sixth
3:5
If a sound is played with a frequency of 480 Hz, and a second sound is played with a frequency of 800 Hz,
what is the name of the musical interval between the two sounds?
A. Major third
B. Perfect fourth
C. Perfect fifth
D. Major sixth
3. (ACT/SAT) Multiple choice - A tree specialist is called in to treat a large apple orchard of problematic trees
exhibiting multiple issue. Each tree is analyzed and assigned a primary issue. The table below partially
represents the tree specialist’s findings.
Tree Illness by Species
Tree Type
Gala Apple
McIntosh Apple
Granny Smith Apple
Total
If fungus was the primary issue for
Fungus
Bacteria
1280
280
341
687
Parasite
Total
1600
900
3500
3
of the Gala apple trees, how many Gala apple trees had parasites as
4
the primary issue?
A. 66
86
B. 254
C. 334
D. 1200
Problem Solving and Data Analysis
4. (ACT/SAT) Multiple choice – From 1970 to 2000, the use of high-fructose corn syrup as a sugar increased
greatly in the United States. The following incomplete table shows the yearly consumption per capita of
different types of sugar measured in kilograms.
Consumption Per Capita of Different Types of Sugars
1970
1980
1990
2000
Sucrose
46.2
37.9
29.2
29.8
Glucose
8.6
8.9
-9.9
High-Fructose
0.2
8.2
22.5
-Corn Syrup
Total
55.0
-61.6
-From 1990 to 2000 the total amount of sugar consumption per capita increased by 11.4%. As a percentage,
approximately what is the relative frequency of high-fructose corn syrup consumption per capita in the year
2000?
A. 25%
B. 36%
C. 42%
D. 68%
m
5. (ACT/SAT) Multiple choice - The acceleration, a, in meters per second squared  2  due to gravity is 0 at
s 
m
the Earth’s center. It reaches a maximum of 9.7 2 at the surface of the earth approximately 4 thousand
s
miles (mi) from the Earth’s center. If d represents the distance from the Earth’s center in thousands of miles,
which of the following graphs in the da-plane could represent this relationship?
A.
B.
C.
D.
6. (ACT/SAT) Multiple choice – The graph below in the sT-plane shows the temperature, T, of a thermite
reaction s seconds after ignition.
What is the average rate of increase in temperature per second between s = 0 and s = 15 in degrees Celsius
per second?
A. 110
B. 140
Problem Solving and Data Analysis
C. 550
D. 1,650
87
Problems 7 – 9 use the following data set:
20, 22, 23, 23, 25, 28, 30, 30, 31, 34, 40
7. Find the five-number summary for the data set.
8. Create the box plot that represents the data set. Be sure to include the number line for the box plot.
9. If the last number was mistyped and should have been 44, would 44 be considered an outlier? Justify your
answer.
Problems 10 – 12 use the following data set:
40, 45, 46, 50, 51, 51, 53, 54, 56, 60, 62, 67
10. Find the five-number summary for the data set.
11. Create the box plot that represents the data set. Be sure to include the number line for the box plot.
12. What is the cut-off point for a value to be an outlier on the lower end? On the upper end?
13. The length of the land boundary (in thousands of kilometers) of each country in South America is shown
below. Each value is rounded to the nearest thousand kilometers.
Create the box plot that represents the lengths of the land boundaries. Be sure to include the number line for the
box plot.
88
Problem Solving and Data Analysis
 bbl 
14. For each country in East Asia, the average number of barrels of crude oil exported per day 
 is plotted
 day 
bbl
.
below to the nearest 30
day
Select all that Apply – Which of the following quantities have the same value?
A. Minimum
B. Q`1
C. Median
D. Q3
E. Maximum
15. The box-and-whisker plot below shows the average outdoor temperature of a North American City at noon, in
degrees Fahrenheit, for each month of the year.
Approximate the value of the IQR for the average monthly temperature.
Problems 16 and 17 use the following scenario:
The box plot below depicts the numbers of law degrees (JD or LL.B), in thousands, conferred each year in the
United States over a span of 49 years. No two years had duplicate numbers of degrees conferred.
16. Which of the following is closest to the value of the median number of law degrees conferred each year?
A. 9
B. 30
C. 36
D. 39
17. Outliers were not shown when the box plot was created. Did the data set contain outliers? Justify your
answer.
Problem Solving and Data Analysis
89
Problems 18 – 24 use the following scenario:
The box-and-whisker plots below show data on the heights, in meters of all waves measured at an ocean beach
on two separate days.
18. What is the difference of the median wave height from day 1 and the median wave height from day 2, in
meters?
19. Which day has the largest IQR?
A. Day 1
B. Day 2
C. They are the same
D. Impossible to determine
C. They are the same
D. Impossible to determine
20. Which day has the largest range?
A. Day 1
B. Day 2
21. On Day 1, what percent of waves measured between 1m and 1.6m?
22. On Day 1, what percent of waves measured between 1m and 1.8m?
23. On Day 1, what percent of waves measured more than 1.6m?
24. On Day 1, what percent of waves measured less than 1.8m?
90
Problem Solving and Data Analysis
Problems 25 - 41 use the following scenario:
The histogram below
represents
the ages of the first twenty Academy Award winners for Best
Actress.
Histogram
Collection
1
12
10
First 20 Best Actress
Winners
B
Count
8
6
C
4
D
A
E
2
20
25
35
30
40
F
45
50
55
65
60
70
Age
The bins of the histogram have been labeled A, B, C, D, E, and F. For each value below, identify the bin in which
the value lies. If the value does not belong in any of the bins, select ‘none of these’.
Question
Number
Value
25
18
A
B
C
D
E
F
none of these
26
20
A
B
C
D
E
F
none of these
27
23
A
B
C
D
E
F
none of these
28
25
A
B
C
D
E
F
none of these
29
32
A
B
C
D
E
F
none of these
30
34
A
B
C
D
E
F
none of these
31
36
A
B
C
D
E
F
none of these
32
40
A
B
C
D
E
F
none of these
33
42
A
B
C
D
E
F
none of these
34
45
A
B
C
D
E
F
none of these
35
54
A
B
C
D
E
F
none of these
36
60
A
B
C
D
E
F
none of these
37
65
A
B
C
D
E
F
none of these
Bin
38. Select all that Apply - How many winners could be exactly 36 years old?
A. 0
B. 1
C. 2
D. 3
E. 4
39. What is the highest possible age of an Academy Award winner for Best Actress?
40. What is the lowest possible age of an Academy Award winner for Best Actress?
41. Between which two values does the median age of an Academy Award winner for Best Actress fall?
Problem Solving and Data Analysis
91
42. The histogram below shows the number of vehicles that a car rental agency currently has available to rent,
categorized by fuel efficiency ratings.
C
B
A
D
In which bin does the median fuel efficiency rating fall?
Problems 43 – 45 use the following scenario:
The AT&T store in Crown Point, Indiana has 15 male employees and 15 female employees. The store kept track
of the number of new cell phones sold by each employee in the month of March. The data for each gender is
shown in the histograms below.
43. Which gender has a larger median value?
44. Which gender has a larger range of values?
45. The most number of employees (male and female combined) sold how many phones?
A. Between 10 and 19 inclusive
B. Between 20 and 29 inclusive
C. Between 30 and 39 inclusive
D. Between 40 and 49 inclusive
92
Problem Solving and Data Analysis
Practice Set 16 – Shapes and Effects
Calculator Required
Objectives
 Classify the shape of a distribution and explain how the shape affects the mean of the data set.
Notes



Skewed Left
Skewed Right
Symmetric
1. (ACT/SAT) A farmer plants wheat in a rectangular plot of land having a length of 7260 feet and a width of 1200
feet. If the farmer makes a profit of $30 per acre, how much profit should he expect to make from the wheat
planted, in dollars? (1 acre = 43,560 square feet)
2. (ACT/SAT) Multiple choice – Tyrone and Jennifer are comparing two songs that they composed. Tyrone’s
song has 90 beats per minute, and Jennifer’s song has
7
1
beats per second. If both songs are 3 minutes
4
2
long, then whose song has more total beats?
A.
B.
C.
D.
Tyrone’s song has more total beats.
Jennifer’s song has more total beats.
The two songs have an equal number of total beats.
There is not enough information to determine which song has more total beats.
3. (ACT/SAT) Multiple choice - An Analyst at an environmental agency is investigating the usage of recycle
paper in various industries. The analyst’s preliminary findings are partially tabulated in the table below.
Average Recycled
Content
0%-25%
25%-50%
50%-75%
75%-100%
Companies’ Recycled Paper Usages by Industry
Packing Materials
Newspapers and
Food Related
Manufacturers
Magazines
Paper Products
-------------
Total
If exactly
40
40
40
Total
---54
120
1
of the food related paper product companies fell into the 75%-100% average recycled content
2
category, what is the expected probability that a company in the 75%-100% range was a food related paper
products company?
A.
1
6
B.
10
27
Problem Solving and Data Analysis
C.
27
40
D.
10
9
93
4. (ACT/SAT) Multiple choice – The table below shows the amount of organic foods sold by different types of
grocery stores in billions of dollars.
Organic Foods Sold in Grocery Stores in Billions of Dollars
Type of Grocery Store
1991
2000
Conventional
--Natural
$0.68
$3.82
Other
$0.25
$0.23
In 1991, conventional grocery stores sold 7% of all organic foods whereas in 2000, conventional grocery
stores sold 48% of all organic foods. In billions of dollars, approximately how much more organic food was
sold by conventional grocery stores in 2000 compared to 1991?
A. 1.88
B. 3.14
C. 3.67
D. 4.31
5. (ACT/SAT) Multiple choice - The plot below in the Th-plane shows how the height, h, in inches (in) of the first
bounce of a ball dropped from 3 feet depends on the temperature, T, in degrees Fahrenheit  F  .
What is the significance of the value h = 27 as shown by the dotted line?
A.
B.
C.
D.
The ball reaches a height of 80 in at a temperature of 0F.
The ball reaches a height of 80 in at a temperature of 27F.
The ball reaches a maximum height of 27 in across all temperatures shown.
The ball reaches a maximum height of 27 in approximately 80 in along its trajectory.
6. (ACT/SAT) Multiple choice – The graph below in the ap-plane shows p, the atmospheric pressure of Earth in
pounds per square inch (psi), for a given value of a, the altitude above sea level in kilometers.
The Earth’s atmosphere has the property that there is a fixed distance d such that for any altitude a 0 , the
pressure at an altitude of a0  d is one-half the pressure at an altitude of a 0 . What is the approximate value
of d in kilometers?
A. 1
94
B. 5.6
C. 15
D. 25
Problem Solving and Data Analysis
7. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
8. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
9. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
10. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
Problem Solving and Data Analysis
95
11. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
C. Skewed Right
D. None of these
12. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
13. Describe the shape of the graph below.
A. Skewed Left
B. Roughly Symmetric
14. Describe the shape of the graph below.
A. Skewed Left
96
B. Roughly Symmetric
Problem Solving and Data Analysis
15. The bar graph below summarizes the household size of social worker’s client families.
Which statement best describes the relationship between the mean and median household size?
A. The mean is greater than the median, because there are 2 families with many more than 4 family members.
B. The median is greater than the mean, because there are more families with more than 4 family members than
with fewer members.
C. The mean and median are equal, because there are more than twice as many families with 4 members than
with any other member.
D. There is not enough information to compare the mean and the median.
16. Adult workers in Los Angeles County were surveyed to see how many vehicles were available in their
household. Data was taken separately for males and females in order to compare them.
According to the bar graph above, which of the following is true?
A. The median number of vehicles available to females is greater than the median number of vehicles available
to males.
B. The median number of vehicles available to males is greater than the median number of vehicles available to
females.
C. The median number of vehicles available to females is equal to the median number of vehicles available to
males.
D. There is not enough information to compare the median number of vehicles available to females and males.
Problem Solving and Data Analysis
97
17. The area in thousands of square kilometers of 19 countries in East and Southeast Asia are shown in the dot
plot below. Each value is rounded to the nearest 250 thousand square kilometers.
Which would be greater, the mean or median area?
A.
B.
C.
D.
The mean is larger than the median.
The median is larger than the mean.
The mean and median are approximately equal.
It is impossible to tell because these are rounded values.
18. The box plot below depicts the numbers of law degrees (JD or LL.B), in thousands, conferred each year in
the United States over a span of 49 years. No two years had duplicate numbers of degrees conferred.
Which would be greater, the mean or median number of law degrees conferred?
A.
B.
C.
D.
The mean is larger than the median.
The median is larger than the mean.
The mean and median are approximately equal.
It is impossible to tell.
19. The number of employees in each industry in Seattle was recorded and rounded to the nearest 10 thousand.
The results are displayed in the dot plot below.
Which would be greater, the mean or median number of law degrees conferred?
A.
B.
C.
D.
98
The mean is larger than the median.
The median is larger than the mean.
The mean and median are approximately equal.
It is impossible to tell.
Problem Solving and Data Analysis
20. A police officer recorded the travel speeds, in miles per hour, of traffic on a major arterial road. The
histogram below shows the number of vehicles driving at each speed.
Which would be greater, the mean or median number of law degrees conferred?
A.
B.
C.
D.
The mean is larger than the median.
The median is larger than the mean.
The mean and median are approximately equal.
It is impossible to tell.
21. In San Jose, the amount of time it took each person to get to work was recorded and rounded up to the
nearest 5 minutes. The data collected for men and women are shown in the bar graph below.
According to the bar graph, which of the following comparisons is true?
A.
B.
C.
D.
The mean travel time for men is greater than the mean travel time for women.
The mean travel time for women is greater than the mean travel time for men.
The median travel time for men is greater than the median travel time for women.
The median travel time for women is greater than the median travel time for men.
Problem Solving and Data Analysis
99
Practice Set 17 – Standard Deviation
Calculator Required
Objectives
 Understand what standard deviation (variance) represents given a set of data or graph.
 Compare the standard deviation of multiple data sets.
Notes
 Spread
 Standard Deviation
 Variance
1. (ACT/SAT) 3.01-3.13 A commercial real estate developer creates a scale drawing of a commercial property
that he hopes to sell. The ratio of the area of the drawing to the actual area of the commercial property is
1 ft 2 : 900 ft 2 . The developer hopes to sell the commercial space for $1,800,000, which would be equivalent
to $1000 per 1 square foot  ft 2  of the property’s area. To the nearest square foot, what is the area of the
scale drawing?
 N 
2. (ACT/SAT) Multiple choice – 3.01-4.5 Stress, measured in newtons per square meter  2  , is the ratio of
m 
force, in newtons (N) to the area, in square meters  m2  on which that force is acting. Based on the table
below, which object is experiencing the greatest stress?
A. Object 1
Object
Force (N)
Object 1
Object 2
Object 3
72
185
406
Object 4
512
B. Object 2
Area  m2 
6.46  10 5
4.56  10 5
5.07  10 4
1.14  10 3
C. Object 3
D. Object 4
3. (ACT/SAT) Multiple choice - 3.04-3.9 A number of commercially available food and vitamin supplements
were tested for heavy metal content. The table below partially represents the supplements that were tested
and whether their lead levels are considered safe.
Lead Levels in Food and Vitamin Supplements
Vitamin C
Vitamin B12
Omega-3 (plant source)
Omega-3 (animal source)
Protein (plant source)
Safe lead levels
----11
Unsafe lead levels
21
---9
Total
--86
---
Protein (dairy source)
18
6
-Fish Oil
-17
-Total
168
-307
If about 41% of vitamin C supplements are found to have unsafe lead levels, how many vitamin C
supplements were tested, in total?
A. 9
100
B. 51
C. 57
D. 126
Problem Solving and Data Analysis
4. (ACT/SAT) Multiple choice – 3.04-4.5 In a study of image processing, participants were shown an image that
could be seen either as a duck or a rabbit. The following table shows the participants’ responses according to
their dominant writing hand.
Dominant Writing Hand
Duck
Rabbit
Total
Right
1,916
779
2,695
Left
331
120
451
Total
2,247
899
3,146
Based on the data, is there evidence that participants’ dominant writing hand is independent of whether they
see the image as a duck?
A. No, because approximately 86% of the participants are right-handed.
B. No, because out of the participants who saw the image as a duck, 1,585 more right-handed participants
saw the image as a duck compared to left-handed participants.
C. Yes, because approximately 71% of participants that are right-handed, 73% of participants that are lefthanded saw the image as a duck, and overall 71% of participants saw the image as a duck.
D. Yes, because overall, there were 1,348 more participants who saw the image as a duck rather than a
rabbit.
5. (ACT/SAT) Multiple choice - 3.06-3.11 Bibb lettuce is grown hydroponically using water and a mixture of
nitrates. The mass, m, in grams (g) of a mature head of lettuce growing in a nitrate concentration, C, in
g
grams per liter   is plotted at various concentrations. The mass reaches a maximum at a concentration
L 
g
g
. Only once the concentration is at least 40 is the lettuce unable to grow, and therefore, has a
L
L
mass of 0 gm. Which of the following plots in the Cm-plane could represent this situation?
of 15
A.
B.
C.
D.
6. (ACT/SAT) Multiple choice – 3.06-3.12 The graph below in the ta-plane shows the horizontal acceleration, a,
m
in meters per second per second  2  of an elastic ball thrown against a wall t milliseconds (ms) after it
s 
impacts the wall.
What is the significance of the graph at t = 15 ms?
A.
B.
C.
D.
The elastic ball touches the wall for 30 ms.
The elastic ball reaches its greatest horizontal speed 15 ms after impact.
The elastic ball experiences the greatest horizontal acceleration 15 ms after impact.
The elastic ball experiences the greatest horizontal acceleration 15 ms after being thrown.
Problem Solving and Data Analysis
101
Problems 7 and 8 refer to the following lists of data:
List 1: 20, 23, 24, 24, 25, 26, 27, 29, 30
List 2: 10, 14, 17, 20, 25, 26, 29, 39, 45
List 3: 23, 23, 24, 25, 25, 25, 26, 26, 27
7. Which of the three lists above has the largest standard deviation? Justify your answer.
8. Which of the three lists above has the smallest standard deviation? Justify your answer.
9. The AT&T store in Crown Point, Indiana has 15 male employees and 15 female employees. The store kept
track of the number of new cell phones sold by each employee in the month of March. The data for each
gender is shown in the histograms below.
Which gender has a larger standard deviation for the number of new cell phones sold? Justify your answer.
10. The dot plots below show the student height distributions of two different 11th grade math classes. Which of
the data sets has a greater standard deviation? Justify your answer.
102
Problem Solving and Data Analysis
11. A study was done to compare the number of points that the Chicago Bulls scored in the first 30 games of the
2013 and 2014 seasons. The histograms below represent the data that was collected.
In which season was the standard deviation of points scored greater? Justify your answer.
Problems 12 and 13 use the following scenario:
The histogram below shows the average life span (in years) for a variety of animals.
Histogram
Collection 1
Animal Life Span
10
Count
8
6
4
2
10
15
20
25
30
35
Lif eSpan
40
45
50
55
60
12. If two more animals were added to the histogram and each had an average life span of 62 years, how would
the standard deviation of the average life span change?
A.
B.
C.
D.
Standard deviation would increase.
Standard deviation would decrease.
Standard deviation would stay the same.
This is impossible to computer without knowing the actual values from the histogram.
13. If two more animals were added to the histogram and each had an average life span of 22 years, how would
the standard deviation of the average life span change?
A.
B.
C.
D.
Standard deviation would increase.
Standard deviation would decrease.
Standard deviation would stay the same.
This is impossible to computer without knowing the actual values from the histogram.
Problem Solving and Data Analysis
103
14. The boxplots below show the distribution of Western Civilization test scores for two different classes.
Which of the classes had the larger standard deviation of test scores?
A. Class A
B. Class B
C. They are equal.
D. Impossible to determine
Problems 15 and 16 use the following scenario:
A consumer testing company studied several brands of electric stoves to see how long it took to boil 4 cups of
water in a covered saucepan at the highest burner setting. Each stove was tested 20 times. The boxplots below
show the results of this study.
15. Which of the stoves has the smallest standard deviation?
A. Stove A
B. Stove B
C. Stove C
D. Stove D
16. Which of the stoves has the largest standard deviation?
A. Stove A
B. Stove B
C. Stove C
D. Stove D
17. The number of homework assignments completed by students in two classes is represented in the boxplot
below.
Which of the classes had the largest standard deviation? Justify your answer.
104
Problem Solving and Data Analysis
18. Below represents the average gas price in the Chicago area during the years 2013-2015.
2015
2014
2013
Which of the years above had the largest standard deviation? Justify your answer.
19. A manufacturer developed two new types of light bulbs. Extensive testing was conducted to see how long
the light bulbs would last under normal usage. The results were combined into the boxplots below.
Which type of light bulb has the smallest variance? Justify your answer.
20. The number of structures built in each decade in Denver County is shown in the histogram below.
Data for years before 1940 or after 2009 was not collected. Which of the following statements about the
shape of the number of structures built is true?
A.
B.
C.
D.
It is bell-shaped because most structures were built in the 1950-1959 decade.
It is bell-shaped because most structures were built in the 1970-1979 decade.
There is little variance in the shape.
There is a lot of variance in the shape.
Problem Solving and Data Analysis
105
21. The histogram below represents the gas efficiency of cars in the student parking lot. What is the maximum
number of cars which get 20 miles per gallon of gas?
Select all that Apply – Which of the following would increase the standard deviation?
A.
B.
C.
D.
Adding more cars that get less than 10 miles per gallon.
Adding more cars that get around 18 miles per gallon.
Adding more cars that get more than 25 miles per gallon.
Removing cars from the data set that get more than 25 miles per gallon.
Problems 22 and 23 use the following scenario:
The histogram below shows the quantity of chocolate pieces per bag of trail mix.
0
20
40
60
80
100
22. What would happen to the standard deviation if the three bags with the lowest number of chocolate pieces
were removed from the histogram?
A.
B.
C.
D.
Standard deviation would increase.
Standard deviation would decrease.
Standard deviation would stay the same.
This is impossible to determine without eating some of the trail mix.
23. What would happen to the standard deviation if the three bags whose number of chocolate pieces were in the
40s were removed from the histogram?
A.
B.
C.
D.
106
Standard deviation would increase.
Standard deviation would decrease.
Standard deviation would stay the same.
This is impossible to determine without eating some of the trail mix.
Problem Solving and Data Analysis
Practice Set 18 – Data Collection and Conclusions
Calculator Required
Objectives
 Classify a scientific study as an experiment, observation study, or sample survey.
 Identify components of a scientific study and what conclusions can be drawn.
Notes







Control/Control Group
Experiment
Experimental Group
Observational Study
Placebo
Sample Survey
Treatment
1. (ACT/SAT) New York City has a population density of 27,000 residents per 1 square mile. The area of New
York City is 301 square miles, and there is approximately 1 subway car for every 1,300 New York City
residents. Rounded to the nearest one hundred subway cars, approximately how many total subway cars
are in New York City?
2. (ACT/SAT) Multiple choice – A paver needs a mix such that the water to concrete ratio, as a decimal, is less
than 0.5 for durability but greater than 0.35 for workability. Which of the mixes in the table below meets the
paver’s requirements?
Mix
Mix 1
Mix 2
A. only mix 1
Pounds of Concrete
50
80
B. only mix 2
Pounds of water required
19
34
C. both mix 1 and mix 2 D. neither mix 1 nor mix 2
3. (ACT/SAT) Multiple choice - A particular galaxy is being used in a study of star formation. The table below
partially represents the study’s preliminary observations of star age vs. distance from the galaxy’s center.
Star Age vs. Distance from Galaxy’s Center
Age
<800
800 to 1500
> 1500
(in billions of years)
light years
light years
light years
0–2
--230
2 – 10
> 10
Total
----
----
--515
Total
424
213
481
1118
If about 13% of the stars included in the table were older than 10 billion years and also over 1,500 light years
from the galaxy’s center, approximately how many stars is this?
A. 63
B. 67
Problem Solving and Data Analysis
C. 145
D. 973
107
4. (ACT/SAT) Multiple choice – A quality control specialist is examining the number of defective components
formed under two different manufacturing methods. The table below shows the number of defective and
adequate components in a study of both methods.
Manufacturing Method Defective Adequate
Total
Method 1
22
20,200
20,222
Method 2
18
8,400
8,418
Total
40
28,600
28,640
Based on the data, is there evidence that the manufacturing method is independent of whether the
components are defective?
A. No, because there were 11,800 more adequate components produced by Method 1 compared to Method
2.
B. No, because the probability of producing a defective component overall is approximately 1.4  10 3 ,
whereas the probability of Method 2 producing a defective component is approximately 2.1  10 3.
C. Yes, because there were only 4 more defective components in Method 1 compared to Method 2.
D. Yes, because the overall probability of producing a defective component is approximately 1.4  10 3 , and
the probability of Method 2 producing a defective component is approximately 2.1  10 3.
5. (ACT/SAT) Multiple choice - The graph below in the sT-plane shows the temperature, T, in degrees
Fahrenheit  F  of an incandescent light bulb s seconds after being initially turned on from a temperature of
50F .
While on, the temperature was always increasing. Less than a minute after being turned on, the light bulb
was turned off and its temperature started decreasing. By approximately how many degrees Fahrenheit did
the light bulb’s temperature increase while being turned on?
A. 30
B. 125
C. 225
D. 275
6. (ACT/SAT) Multiple choice – An electromagnetic pulse is generated and its profile at a distance D, in
micrometers  m  , is taken 1 picosecond later. The magnetic field, M, in nanoteslas (nT) reaches a
minimum of 4nT at a distance of 50 m from the source. The magnetic field reaches a maximum of 10 nT
at a distance of 90 m . Which of the following graphs in the DM-plane could represent this situation?
A.
108
B.
C.
D.
Problem Solving and Data Analysis
7. Field researchers in Africa want to determine and compare the socialization habits and behavior of two groups
of gorillas: mountain gorillas and eastern lowland gorillas. Researchers will visit selected families of wild
gorillas every day until they are confident enough that these gorillas can be approached. The researchers will
watch the families and record their social habits and behavior. Which of the following is the best description of
this type of research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A controlled experiment, a study in which an investigator separates subjects into a control group that does not
receive a treatment and an experimental group that receives a treatment, and then observes the effect of the
treatment on the experimental group.
C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or
interview, in order to estimate population attributes.
D. None of the above
8. A consumer agency wants to determine information about smartphone use in the United States. Participants
will be selected using random digit dialing (RDD), a method for selecting people for involvement in telephone
statistical surveys by generating telephone numbers at random. Questionnaires will then be distributed every
day for two weeks to track smartphone use. Which of the following is the best description of this type of
research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or
interview, in order to estimate population attributes.
C. A controlled experiment, a study in which an investigator separates subjects into a control group that does not
receive a treatment and an experimental group that receives a treatment, and then observes the effect of the
treatment on the experimental group.
D. None of the above
9. The U.S. National Park Service conducted a study at a national park in the Northeast to determine which
marsh habitats were especially valuable for species diversity, which supported high breeding densities, and
which supported regionally uncommon species. Scientists surveyed the avian communities at two different
wetlands within the national park to identify those areas of the wetlands that are the most ecologically valuable
bird habitats. Which of the following is the best description of this type of research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or
interview, in order to estimate population attributes.
C. A controlled experiment, a study in which an investigator separates subjects into a control group that does not
receive a treatment and an experimental group that receives a treatment, and then observes the effect of the
treatment on the experimental group.
D. None of the above
Problem Solving and Data Analysis
109
10. In order to determine whether children who have just watched cartoons will perform better on cognitive tasks
than children who have not just watched cartoons, researchers randomly divided 60 preschoolers into two
groups. For nine minutes, one group watched a rapid-paced cartoon, while the other group did not watch
anything and did a quiet activity. They then administered standardized tests to determine the immediate
impact of the children’s previous nine minutes of activity. Which of the following is the best description of this
type of research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A controlled experiment, a study in which an investigator separates subjects into a control group that does
not receive a treatment and an experimental group that receives a treatment, and then observes the effect of
the treatment on the experimental group.
C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire
or interview, in order to estimate population attributes.
D. None of the above
11. A researcher’s hypothesis is that adults who exercise 10 or more hours per week are less likely to develop
colds than adults who do not exercise. The research plans to assemble a group of 1,000 adults that do not
exercise but otherwise are in good health as subjects. During the study, these adults will exercise for 10 or
more hours per week for one year, with the researcher collecting cold data throughout the year. Which of the
following is the best description of the research design for this study?
A.
B.
C.
D.
Observational study
Sample Survey
Controlled experiment
None of the above
12. In the year 1975, Janet Starkes devised an “occlusion” test to determine whether there are differences
between the elite and novice women volleyball players. Players of different levels were asked to look at
slides for a fraction of a second showing women volleyball players in action. Starkes then asked the players
whether the ball was in the frame or not in the frame. She found an enormous difference between elite
volleyball players and novices: elite players could determine in a fraction of a second whether the ball was
inside the frame or not. This was not the case for novice players. Which of the following is the best
description of this type of research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A controlled experiment, a study in which an investigator separates subjects into a control group that does
not receive a treatment and an experimental group that receives a treatment, and then observes the effect of
the treatment on the experimental group.
C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire
or interview, in order to estimate population attributes.
D. None of the above
13. A local bank with two branches wants to determine which of two methods of serving customers during peak
hours is more efficient. There are 5 tellers available during peak hours. The first method has customers form
a single line, and the first in line is the first served. The second method has customers form 5 individual lines,
one for each teller. Which of the following is the best way to prove one method is superior to the other?
A.
B.
C.
D.
110
Observational study
Sample Survey
Controlled experiment
None of the above
Problem Solving and Data Analysis
14. An ecologist measured the population of brown bears in a North American region and the number of
deforested acres in the same region since the year 2000. The study concluded that as the population of
brown bears steadily decreased, the number of deforested acres steadily increased during the same time
period. Which of the following is the best way to prove one method is superior to the other?
A.
B.
C.
D.
Observational study
Sample Survey
Controlled experiment
None of the above
15. A local tv news station wants to determine how often and through which medium their viewers check the
weather. Which of the following survey methods is most likely to produce valid results?
A. Ask a random sample of their viewers how much they enjoy the weather portion of the local news.
B. Ask a random sample of their viewers whether they own a smartphone.
C. Ask a random sample of members of the local meteorological society whether they watch the local news.
D. Ask a random sample of their viewers how often and when they use various sources to obtain weather
information.
16. A researcher wants to conduct a survey to gauge United States (US) voters’ opinions about US Congress.
Which of the following should NOT be a component of this survey?
A.
B.
C.
D.
The researcher collects data from the survey takers.
The researcher analyzes data from the survey takers.
The researcher distributes the survey to 10,000 randomly selected US citizens aged 18 and older.
The researcher distributes the survey to 10,000 residents of a Washington D.C. neighborhood.
17. A local package delivery service wants to improve the efficiency of its deliveries. As a first step, the
management team decides to conduct a study to determine the average length of time from the arrival of a
package at the company’s mail center until its delivery at a home. Which of the following methods is most
likely to produce valid results?
A. The team selects the 1,000 heaviest packages in a one-week, non-holiday period and records how long it
takes for each package to reach its destination.
B. The team calls 1,000 residents in their delivery area and asks them whether they have received a package
from their service in the past week. They will then record how long it took for those packages to reach their
destination.
C. The team selects a random sample of 1,000 packages arriving at the center over a one-week, non-holiday
period and records how long it takes for each package to reach its destination.
D. None of the above
18. A local tv news station wants to determine how often and through which medium their viewers check the
weather. Which of the following survey methods is most likely to produce valid results?
A. Ask a random sample of their viewers how much they enjoy the weather portion of the local news.
B. Ask a random sample of their viewers whether they own a smartphone.
C. Ask a random sample of members of the local meteorological society whether they watch the local news.
D. Ask a random sample of their viewers how often and when they use various sources to obtain weather
information.
Problem Solving and Data Analysis
111
19. The graph shown below describes the modes of transportation used by U.S. workers to travel to work for the
years 2008-2012 combined.
Which conclusion is best supported by the results of this study?
A. In the year 2012, about 86% of U.S. workers used cars, trucks, or vans to travel to work.
B. Less than 20% of U.S. workers used modes of transportation other than cars, trucks, or vans in 20082012.
C. More people walked to work in 2008-2012 than rode bicycles because people lived close enough to work
to walk.
D. People used cars, trucks, or vans more than other modes of transportation because of reduced gas
prices.
20. A survey of moviegoers asked a random sample of over 1,500 people which snack they preferred while
watching movies. The results are shown below.
Based on the data, which conclusion is valid?
A.
B.
C.
D.
112
People do not like to eat pizza at the movies because it is messy.
Less than 10% of people surveyed preferred candy at the movies because of the sugar content in candy.
About six times as many people surveyed preferred popcorn to candy.
None of the above.
Problem Solving and Data Analysis
21. An ad impression is the display of an ad to a user while viewing a web page, and a vertical market is one that
serves the needs of a particular industry. The graph below shows the three highest and lowest vertical
market percent increases for global mobile ad impressions in the fourth quarter of 2011.
Based on the results of this study, which conclusion is best supported by the data?
A. Advertisers do not use mobile ads because too few people access information in this manner.
B. Mobile ad impressions for shopping increased more than twice as much as those for sports.
C. Mobile ad impressions are increasing at a rapid rate because more people globally have access to mobile
connections than other internet connections.
D. Mobile ad impressions are increasing at a greater rate than other online platforms.
22. The table below shows the results of an observational study designed to observe the social media habits of
different age groups of internet users in the U.S. between 2005 and 2013.
Based on the results of this study, which of the following conclusions are valid?
I. In each year of the student, U.S. internet users aged 18-29 were more likely to use social media than any other
age group in the study.
II. Over the course of the study, there was growth in the percentage of U.S. internet users that use social media
across all of the age groups observed.
III. The rate of social media use by U.S. internet users will continue to rise in the future.
IV. Social media was more likely to be used by a U.S. internet user aged 30-49 in 2013 than it was by a U.S.
internet user aged 30-49 in 2005.
A. I only
B. I and IV only
Problem Solving and Data Analysis
C. I, II, and IV
D. I, II, III, and IV
113
23. The table below shows the results of a controlled experiment designed to determine the effect that adding
sodium chloride to water has on the boiling point of water at sea level.
Based on the results of this experiment, which conclusion is NOT valid when up to three tablespoons of
sodium chloride are added to one quart of water?
A. The more sodium chloride that is added to water, the higher the water’s boiling temperature becomes.
B. The more sodium chloride that is added to water, the longer the water will take to boil.
C. There is an association between adding sodium chloride to water and an increase in the boiling
temperature of water.
D. There is a linear relationship between sodium chloride added to water and the water’s boiling temperature.
24. Louis Pasteur conducted a famous experiment that addressed the question: “Can microorganisms generate
spontaneously?” To replicate the experiment, in the control group, purify water in closed flasks by boiling
them, and then let the water sit in the closed flasks at room temperature for a predetermined period of time.
In the experimental group, purify water in identical closed flasks by boiling them. However, before letting the
experimental group sit at room temperature for the predetermined period of time, break the top stem of these
flasks to expose the water to outside elements. After the predetermined period of time, if no microorganisms
are observed in the control flasks and several thousand microorganisms are observed in each experimental
flask, which of the following conclusions are valid?
I. When closed off to outside elements, purified water will not spontaneously generate microorganisms.
II. Exposing water to the elements causes the water to become harmful to humans.
III. Breaking the top stem of the experimental flask allowed the microorganisms to enter the purified water.
IV. Not breaking the stem of the control flask prevented microorganisms from entering the purified water
within.
A. III only
B. III and IV only
C. I, III, and IV
D. I, II, III, and IV
25. In a variation of the famous “marshmallow test” first conduct in the 1970s, psychologists randomly assigned
children aged three to five years old to one of two experimental conditions – “reliable” and unreliable”. In the
reliable group, the adults had previously delivered something they had promised to the children. In the
unreliable group, the adults had not delivered something they had promised. The children were then told by
the adults that they could either have one marshmallow now, or two marshmallows if they could wait a short
amount of time (15 minutes maximum). The researchers found that children who experienced the reliable
interaction with adults waited four times longer (12 versus 3 minutes on average) than children in the
unreliable situation. Based on the results, which of the following conclusions are valid?
I. Children who can wait longer for the second marshmallow do better later in life.
II. Adults who do not follow through on their promise cause children to be more reliable.
III. There is convincing evidence that perceived reliability of an adult causes children to have more patience.
IV. Children who can wait for the second marshmallow have higher scores on standardized tests.
A. III only
114
B. III and IV
C. I, III, and IV
D. I, II, III, and IV
Problem Solving and Data Analysis
26. The table below shows the results of a controlled experiment designed to determine the effect of tailgate
position on the fuel consumption of a pickup truck.
Based on the results of this experiment, which conclusion is NOT valid?
A. The truck needed the least fuel to travel a set distance when its tailgate was all the way up.
B. The truck needed the most fuel to travel a set distance when its tailgate was all the way down.
C. There is an association between the truck’s tailgate position and the amount of fuel needed to travel a set
distance.
D. A truck drive who drives with the tailgate up will spend less money on fuel than when the truck driver
drives with the tailgate down.
27. The table below shows the percentages of the Canadian population as well as the percentage of Canadian
hockey players in the National Hockey League (NHL) residing in cities of various sizes.
Based on the results of this study, which conclusion is best supported by the evidence?
A. There is evidence that players from mid-sized cities (100,000-499,999) are overrepresented in the NHL.
B. Players from very small communities (<1,000) do not have as many opportunities for elite training as
players from larger communities.
C. Cities with populations larger than 500,000 are underrepresented in terms of players in the NHL because
players in these communities face too much competition.
D. Players in large cities have more opportunities for elite training than do players from smaller cities.
Problem Solving and Data Analysis
115
Practice Set 19 – Assessment 4 Review – 60 Points
1. (ACT/SAT) Two friends rented a table at a ping pong parlor. The table cost them $10 for every 30 minutes of
play time and the friends spent $40.00 in total. On average, the friends played 1 ping pong game every 20
minutes. How many ping pong games did the friends play?
2. (ACT/SAT) Multiple choice – A marine aquarium has a small tank and a large tank, each containing only red
and blue fish. In each tank, the ratio of red fish to blue fish is 3 to 4. The ratio of fish in the large tank to fish
in the small tank is 46 to 5. What is the ratio of blue fish in the small tank to red fish in the large tank?
A. 15 : 184
B. 10 : 69
C. 69 : 10
D. 184 : 15
3. (ACT/SAT) Multiple choice - A university collects data regarding their alumni who earned degrees in science
or engineering and are currently employed in either academia or private industry. The results are partially
tabulated in the table below.
Science Degrees and Employment
Academia
Industry
Total
Science
--943
Engineering
--1597
Total
1367
1173
2540
About how many alumni with science degrees should be employed in academia in order to provide evidence
that working in academia is independent of degree earned?
A. 350
B. 430
C. 500
D. 730
4. (ACT/SAT) Multiple choice – An online book store conducted a survey about book preference with respect to
different age groups. One question on the survey asked participants whether they preferred the Harry Potter
series or the Twilight series.
Survey of Book Preferences by Age
Age
Harry Potter Twilight
Young Adults (13-20)
1,539
216
Total
1,755
Adults (21+)
1,161
84
1,245
Total
2,700
300
3,000
Based on the data shown in the table above, is there evidence to suggest that whether participants preferred
the Harry Potter series or the Twilight series is independent of the participants’ age group?
A. No, because 57% of the participants who preferred the Harry Potter series were young adults, whereas
72% of the participants who preferred the Twilight series were young adults.
B. No, because of the participants who preferred the Twilight series there are 132 more young adults than
adults.
C. Yes, because in both the young adult group and the adult group, there are approximately 1,000 less
participants who prefer the Twilight series.
D. Yes, because 88% of young adults preferred the Harry Potter series, 93% of the adults preferred the Harry
Potter series, and 90% of all participants preferred the Harry Potter Series.
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Problem Solving and Data Analysis
5. (ACT/SAT) Multiple choice - The National Retail Federation introduced the term “Cyber Monday” in 2005 to
describe a sharp rise in online revenue and traffic the first Monday after Thanksgiving. The graph below in
the tr-plane approximates the total revenue, r, in millions of dollars, from Cyber Monday sales in the year t
years after 2009.
What is the best interpretation of the portion of the graph to the left of the r-axis?
A.
B.
C.
D.
It refers to loss of revenue.
It refers to revenue in years before 2009.
It is irrelevant, because you cannot have negative revenue.
It is irrelevant, because there were no Cyber Monday sales before 2009.
6. (ACT/SAT) Multiple choice – Using the doppler effect, astronomers can determine the frequency of light, f(v),
in terahertz (THz) emitted from a galaxy with a velocity in the direction toward Earth of v, as a fraction of the
speed of light c. It is true that galaxies with a velocity of 0 toward Earth emit light with a positive frequency,
and frequency is never 0 THz for any velocity. Additionally, as the velocity toward Earth increases, the
frequency of light emitted increases. Which of the following could represent the graph of y = f(v) in the vyplane?
A.
B.
Problem Solving and Data Analysis
C.
D.
117
Section 13 – Data Inferences (15 pts) (Calculator Required/No Calculator)
 Create and interpret a confidence interval
 Understand the effect that the confidence level and sample size has on the margin of error
 Find the margin of error and sample statistic given a confidence interval
Problems 7 and 8 use the following scenario:
In a study of 40 randomly selected captive Octopus vulgaris, researchers found that the octopi could learn to
integrate visual and tactile information to find food after a mean of 119 trials. The estimate had a margin of error
of 18 trials at a 95% confidence level. Which of the following is the most reasonable conclusion about the number
of trials it would take all captive Octopus vulgaris in general to learn to find the food?
7. Create the 95% confidence interval for the number of trials it would take all captive Octopus vulgaris in general
to learn to find the food.
8. Select all that Apply - Which of the following is a possible value for the actual number of trials it would take all
captive Octopus vulgaris in general to learn to find the food?
A. 79
B. 100
C. 130
D. 159
9. In a particular county, there are 50,000 households. In a sample of the population showed that 84% of the
households lived in the same residence as they had the previous year. The estimate had a margin of error of
1.5% at the 90% confidence level.
Select all that Apply - Which of the following could be an estimate for the number of households that lived in
the same residence as they had the previous year?
A. 41,500
B. 42,000
C. 43,000
D. 43,500
Problems 10 and 11 use the following scenario:
In the 216 National Health and Nutrition Examination Survey, a random sample of 10,000 United States residents
was used to approximate the percent of all United States residents that had healthy levels of high-density
lipoprotein (HDL) cholesterol. The survey reported at the 95% confidence level that between 79% and 82% of all
US residents have healthy levels of HDL cholesterol.
10. What is the value of the sample statistic?
11. What is the value of the margin of error?
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Problem Solving and Data Analysis
Section 14 – Median, Mean and Range (8 pts) (Calculator Required/No Calculator)
 Calculator the mean, median, and range from various representations of data
 Analyze the effects changing a data will have on the mean and median
Problems 12 – 14 use the following scenario:
The dot plot below depicts the number of bananas per cluster for a sample of banana clusters.
12. What is the median number of bananas per cluster?
13. To the nearest banana, what is the mean number of bananas per cluster?
14. What is the range of the number of bananas per cluster?
Problems 15 – 18 use the following scenario:
The table below partially records the numbers of pairs of socks manufactured by a company each quarter.
Quarter
Pairs of socks
manufactured
A
B
C
D
E
F
G
H
I
10,765
12,268
12,729
11,568
11,830
13,480
11,345
15,072
?
15. What is the median number of pairs of socks manufactured in quarters A – H?
16. What is the mean number of pairs of socks manufactured in quarters A – H? Round your answer to the
nearest pair of socks.
17. What is the range of the number of pairs of socks manufactured in quarters A – H?
18. If the median of all 9 quarters (A – I) is 11,830, and the range is the same with and without quarter I, which of
the following could be the number of pairs of socks manufactured in quarter I?
A. 8,962
B. 10,816
Problem Solving and Data Analysis
C. 12,739
D. 15,511
119
19. The time, in minutes, rounded to the nearest minute, that runners took to finish a 3-mile race is shown in the
table below.
Time in minutes
18
19
20
21
22
23
24
Number of runners
1
2
3
6
r
1
2
If the mean finish time was 21 minutes, what is the value of r in this table?
A. 6
B. 3
C. 2
D. 1
20. Both dot plots below show the years in which various New Zealand wineries were founded.
The first dot plot rounds these values to the nearest 10 years, and the second dot plot rounds these values
to the nearest 20 years. If we calculate the mean, median, and range based on each of the dot plots and not
from the original data used to generate them, which of them will differ from the first dot plot to the second?
A.
B.
C.
D.
None will differ.
Mean only
Mean and median only
Mean, median, and range
Section 15 – Boxplots and Histograms (11 pts) (Calculator Required/No Calculator)
 Create and interpret boxplots
 Interpret histograms
 Discuss how changing a data set affects the visual representation of the data set
Problems 21 – 23 use the following scenario:
The box-and-whisker plot below shows the average outdoor temperature of a North American City at noon, in
degrees Fahrenheit, for each month of the year.
21. Find the five-number summary for the average outdoor temperature.
22. Find the value of the IQR for the average outdoor temperature.
23. Should either of the endpoints of the box plot be considered an outlier? Justify your answer.
120
Problem Solving and Data Analysis
Problems 24 – 27 use the following scenario:
The box-and-whisker plots below show data on the heights, in meters of all waves measured at an ocean beach
on two separate days.
24. Find the five-number summary for the wave measurements take on day 2.
25. What percent of day 2 waves measured less than 2 meters?
26. What percent of day 1 waves measured more than 1 meter?
27. What is the cutoff value for a wave measured on day 2 to be a large outlier?
Problems 28 – 32 use the following scenario:
A police officer recorded the travel speeds, in miles per hour, of traffic on a major arterial road. The histogram
below shows the number of vehicles driving at each speed.
28. In which range will the median speed fall?
29. What is the lowest possible speed recorded by the police officer?
30. What is the highest possible speed recorded by the police office?
31. What is the maximum number of cars that could have been traveling exactly 52 mph?
32. How many cars were recorded traveling at 62 mph or higher?
Problem Solving and Data Analysis
121
Section 16 – Shapes and Effects (5 pts) (Calculator Required/No Calculator)
 Classify the shape of a distribution and explain how the shape affects the mean of the data set.
33. A police officer recorded the travel speeds, in miles per hour, of traffic on a major arterial road. The
histogram below shows the number of vehicles driving at each speed.
Which statement best compares the mean and the median of the data?
A. There is no mean value for this data.
B. The mean is greater than the median.
C. The median is greater than the mean.
D. The mean and median are approximately equal.
34. A class tested their reaction times to catch a falling object. The dot plot below gives their results, to the
nearest tenth of a second.
Which statement best compares the median and the mean for this data?
A.
B.
C.
D.
The mean is greater than the median.
The median is greater than the mean.
The mean and the median are about the same.
There is not enough information to determine the mean.
35. The four dot plots below show the student height distributions of four different 11th grade math classes. In
which of the data sets is the mean greater than the median?
122
A.
B.
C.
D.
Problem Solving and Data Analysis
36. A geologist used beryllium – 10 dating on several samples of rock at a site to estimate how long the rock had
been exposed at the surface.
Which of the following best compares the median to the mean of the data?
A.
B.
C.
D.
The median and the mean are approximately equal, because the distribution is symmetric al.
The median is lower than the mean because 2 of the samples are several years older than the rest.
The median is higher than the mean because many more of the samples had 25 years or less of exposure.
There is not enough information to compare the median and the mean.
Section 17 – Standard Deviation (3 pts) (Calculator Required/No Calculator)
 Understand what standard deviation (variance) represents given a set of data or graph.
 Compare the standard deviation of multiple data sets.
37. The histograms below show the test results of two different 11th grade history classes on the same exam.
Which statement best compares the standard deviations of the two data sets?
A. The standard deviation of the scores from class A is greater than the standard deviation of the scores from
class B.
B. The standard deviation of the scores from class B is greater than the standard deviation of the scores from
class A.
C. The standard deviation of the scores from class A is equal to the standard deviation of the scores from
class B.
D. There is not enough information to compare the two standard deviations.
Problem Solving and Data Analysis
123
38. In San Francisco, the number of employees in each occupation was recorded and rounded to the nearest 5
thousand. The results are displayed in the dot plot below.
If each occupation is split into two separate occupations of equal number of employees, then which of the
following occurs?
A.
B.
C.
D.
Only the mean number of employees decreases.
Only the mean and median number of employees decreases.
Only the mean, median, and range of the number of employees decreases.
The mean, median, range, and standard deviation of the number of employees decreases.
39. Below is a histogram of test scores on a biology test.
Select all that Apply – Which of the following would increase the standard deviation of the test scores?
A.
B.
C.
D.
Including more test scores in the 30s
Including more test scores in the 70s
Including fewer test scores in the 70s.
Including three perfect test scores (score of 100).
Section 18 – Data Collection and Conclusions (9 pts) (Calculator Required/No Calculator)
 Classify a scientific study as an experiment, observation study, or sample survey.
 Identify components of a scientific study and what conclusions can be drawn.
40. In a now-famous study, the psychologist and chess master Adriaan de Groot briefly showed several chess
players images of chess positions (for 3-4 seconds), and then asked the players to reconstruct the positions
from memory. He found that grandmasters and masters (highest level) were able to recall the location of 93%
of the pieces, while the experts (next level) remembered 72% and the class players (lowest level) 51%. In
later studies conducted by H. Simon and W. Chase, the experiments were repeated, but in this case with an
additional feature: all the players viewed both real chess positions and random, often impossible, chess
positions. They replicated de Groot’s results for real chess positions, but in the random positions, the players
of all levels did approximately the same. Which of the following is the best description of the research design
for the Simon and Chase study?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A controlled experiment, a study in which an investigator separates subjects into a control group that does not
receive a treatment and an experimental group that receives a treatment, and then observes the effect of the
treatment on the experimental group.
C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire or
interview, in order to estimate population attributes.
D. None of the above
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Problem Solving and Data Analysis
41. A consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum,
glass, and plastic pans in both gas and electric ovens. Which of the following is the best way to prove one
method is superior to the other?
A.
B.
C.
D.
Observational study
Sample Survey
Controlled experiment
None of the above
42. A researcher representing a city government wants to measure public opinion about recycling by asking
1,000 randomly selected residents a series of questions on the subject. Which of the following is the best
description of the research design for this study?
A.
B.
C.
D.
Observational study
Sample Survey
Controlled experiment
None of the above
43. In order to determine whether children who have just watched cartoons will perform better on cognitive tasks
than children who have not just watched cartoons, researchers randomly divided 60 preschoolers into two
groups. For nine minutes, one group watched a rapid-paced cartoon, while the other group did not watch
anything and did a quiet activity. They then administered standardized tests to determine the immediate
impact of the children’s previous nine minutes of activity. Which of the following is the best description of this
type of research design?
A. An observational study, a study in which investigators observe subjects and measure variables of interest
without assigning treatments to the subjects.
B. A controlled experiment, a study in which an investigator separates subjects into a control group that does
not receive a treatment and an experimental group that receives a treatment, and then observes the
effect of the treatment on the experimental group.
C. A sample survey, a study that obtains data from a subset of a population, usually through a questionnaire
or interview, in order to estimate population attributes.
D. None of the above
44. An ecologist wants to conduct an observational study of the impact of the deforestation of a rainforest on an
indigenous species of Tamarin monkey. Which of the following should NOT be a component of this
observational study?
A. The researcher collects data generated by the Tamarin monkeys.
B. The research organizes the monkeys in the rainforest into a control group and an experimental group.
C. The researcher analyzes data generated by the Tamarin monkeys.
D. The research identifies a group of Tamarin monkeys indigenous to the rainforest as the sample population
to be studied.
Problem Solving and Data Analysis
125
45. The graph below shows the results of a study designed to determine the effect of pH on the activity of a
particular enzyme.
Based on the results of this study, which conclusion is best supported by the evidence?
A.
B.
C.
D.
The higher the pH, the greater the enzyme activity.
There is evidence of a linear association between pH and enzyme activity.
There is evidence of an association between pH and enzyme activity that does not appear to be linear.
The lower the pH, the greater the enzyme activity.
46. The graph shown below shows the results of an observational study of corn grain yield, in bushels per acre,
versus rate of nitrogen fertilizer solution, in pounds per acre, applied to crops.
Based on the results of this study, which conclusion is best supported by the data?
A. Using nitrogen in the soil causes greater grain yield.
B. There is evidence of a linear association between the amount of nitrogen applied to the soil and the grain
yield.
C. There is evidence of an association between the amount of nitrogen applied to the soil and the grain yield,
but the association does not appear to be linear.
D. Low levels of nitrogen in the soil leads to poor grain yield.
47. In a survey of smartphone owners, 64% of a random sample of younger adults aged 18-29 used their phones
to listen to music or podcasts, compared to 21% of a random sample of older users who did so. Based on the
results of this survey, which of the following conclusions are valid?
I. Younger adults are more likely to listen to music or podcasts on their smartphones than are older adults.
II. Older adults like music less than younger adults.
III. Older adults do not listen to music on their smartphones because they find it inconvenient.
IV. Younger adults are more likely than older adults to own smartphones.
A. I only
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B. I and II
C. II only
D. I, II, III, and IV
Problem Solving and Data Analysis