Download Math Fundamentals for Statistics II (Math 95) Homework Unit 4

Math Fundamentals for
Statistics II (Math 95)
Homework Unit 4:
Connections
Scott Fallstrom and Brent Pickett
“The ‘How’ and ‘Whys’ Guys”
This work is licensed under a Creative Commons AttributionNonCommercial-ShareAlike 4.0 International License
2nd Edition (Summer 2016)
Math 95 – Homework Unit 4 – Page 1
Table of Contents
This will show you where the homework problems for a particular section start.
4.1: Solving Equations ..........................................................................................................................2
4.2: Lines and Applications ..................................................................................................................6
4.3 Basics of Statistics – Weighted Averages ....................................................................................10
4.4: Likelihood Analysis .....................................................................................................................14
4.5: Critical Thinking with Numbers – Simpson’s Paradox ...........................................................18
4.6: Wrap-up and Review ..................................................................................................................21
4.1: Solving Equations
Vocabulary and symbols – write out what the following mean:

y  mx  b

z
x

Concept questions:
1. When solving 9  x  7 , what operation would you use and why?
2. When solving 9  x  7 , what operation would you use and why?
3. When solving 9  3x , what operation would you use and why?
4. When solving 9 
x
, what operation would you use and why?
3
5. When solving 41  3x  5 , what operations would you use and in what order? Why?
6. When solving 11 
x5
, what operations would you use and in what order? Why?
7
7. How does solving equations relate to the order of operations?
8. Marissa tries to solve 9  x  7 by subtracting 7 from each side to get x by itself. Is this a correct
approach? Write the resulting equation if she did this.
Exercises:
9. Solve the following equations for y, given the value of x.
a. y  2 x  7 , x = 5
d. y  2.5x  7.3 , x = 15.2
b. y  2 x  7 , x = – 5
e. y  2.5x  7.3 , x = 79.52
f. y  2.5x  7.3 , x = – 79.52
c. y  2 x  7 , x   32
Math 95 – Homework Unit 4 – Page 2
10. Solve the following equations for x:
a. 9  2 x  7
b. 19  2 x  7
c. 9  2.5x  7.3
5
x
3
7
k. 5 
x3
7
j.
d. 19  8x  5
e. 493  17 x  244
f.
687 
l.
x  85
11
17 
x 3
5
m. 17  x
g. 17  7 x  3
n. 17  x  5
h. 117  39  6 x
o.  1.3  x  3
i.
17 
x
3
5
11. Solve z 
x  11
when…
2
a. x = 71
e. z = 0.87
b. x = – 25
f. z = – 0.22
c. x = 13.4
g. z = 1.25
d. x = – 5.12
h. z = – 3
12. The formula z 
x

is used in statistics classes where  represents the mean and 
represents the standard deviation. The x is a data value and z is the z-score, representing how
many standard deviations above or below the mean for a particular data value. For the following
problems, use   50 and   10 ; find the z-score and interpret the meaning. The first one is
done for you as an example.
40  50  10

 1 . The z-score is –1, which means that the data value is 1
a. x = 40. z 
10
10
standard deviation below the mean. [This should make sense as one standard deviation is 10,
and the score of 40 is exactly 10 points lower than 50.]
b. x = 30
d. x = 65
c. x = 50
e. x = 19
Math 95 – Homework Unit 4 – Page 3
13. Using the same information as the previous problem, find the data value that is missing (x-value)
if   50 and   10 , and interpret the meaning. The first one is done for you as an example.
x  50
 x  50 
a. z = 1.5. 1.5 
 1.510  
10  15  x  50  15  50  x  50  50  65  x .
10
 10 
A z-score of 1.5 which is 1.5 standard deviations above the mean occurs with a data value of
65.
b. z = 2.3
e. z = – 2.56
c. z = – 1.2
f. z = 3.21
d. z = 0.83
g. z = 0
14. Solve z 
23  
for the missing piece if you know…
1.5
a. z = 2.3
b. z = 0
c. z = – 2
15. Solve 1.2 
x  19

for the missing piece if you know…
d.  = 10
e.  = 3
f.  = 20
a. x = 21
b. x = 25
c. x = 22.6
16. Solve  1.25 
a.  = 20
b.  = 17.5
c.  = 21
d.  = 20
e.  = 25
f.  = 30
15  

for the missing piece if you know…
d.  = 10
e.  = 3
f.  = 20
Math 95 – Homework Unit 4 – Page 4
17. Find the values from the table:
a. What is the body-value associated with a z-score of:
i.
3.33
iii. 2.87
v.
0.11
ii.
2.43
iv.
1.89
vi.
0.35
b. What z-score links with a body-value of…
i.
0.9713
iii. 0.7939
v.
0.9905
ii.
0.9099
iv.
0.8888
vi.
0.5753
c. If you had a body-value of 0.9995, could you determine the z-score or not? Explain why or
why not.
d. If you had a body-value of 0.9840, could you determine the z-score or not? Explain why or
why not.
e. What does a z-score of 0 represent?
f. Does it make sense that the body-value corresponding to a z-score of 0 is 0.5000? Explain.
18. Find the z  corresponding to:
2
a. 90%
b. 80%
c. 60%
Math 95 – Homework Unit 4 – Page 5
  
19. Solve these equations for the missing piece in E  z  
 .
n


2
a. the level of confidence is 99%,   4.35 , and n = 918
b. the level of confidence is 99%,   19.68 , and E = 0.775
c. the level of confidence is 95%,   5.44 , and E = 0.32
d. the level of confidence is 95%, n  544 , and E = 0.45
Wrap-up and look back:
20. Marsha is solving
there was one?
n  25 and gets n = 5. Is she doing this correctly? What was her mistake if
5
 25 and gets n = 5 by dividing 5 on both sides. Is he doing this correctly?
n
What was his mistake if there was one?
21. Michael is solving
22. Write in words what you learned from this section. Did you have any questions remaining that
weren’t covered in class? Write them out and bring them back to class.
4.2: Lines and Applications
Vocabulary and symbols – write out what the following mean:

Slope

y-intercept
Concept questions:
1. If C x   10 x  15 represents the cost (in $) of purchasing x skateboards. What is the slope and
what are the units on the slope?
2. If C x   10 x  15 represents the cost (in $) of purchasing x skateboards. What is the y-intercept
and what are the units on the y-intercept?
3. If C x   10 x  15 represents the cost (in $) of purchasing x skateboards. What does C 10
represent and what are the units on it?
4. Izzie wants to buy 20 skateboards using the previous equation. What is the total price of 20
skateboards? What is the average cost of a skateboard in her purchase?
5. Izzie wants to buy 2 skateboards using the previous equation. What is the total price of 2
skateboards? What is the average cost of a skateboard in her purchase?
6. If you purchased only 1 skateboard from the previous equation, what is the total price and average
price?
Math 95 – Homework Unit 4 – Page 6
7. Based on your previous answers, would you say the total price goes up or down when you
purchase more skateboards? Explain.
8. Based on your previous answers, would you say the average price goes up or down when you
purchase more skateboards? Explain.
Exercises:
9. The following graph shows the value of a collectible car each year that it is driven.
a. Draw a line that best represents the data. As the years go up, the price of the car is
(increasing/decreasing)?
b. Label each axis with the appropriate words and units.
c. Use the line to find the slope and y-intercept. Interpret each of them in the context of the graph.
d. Create a linear equation using the information you found in the previous part.
e. Use your linear equation to approximate the price of the car after 3 years.
f. Use your linear equation to approximate the price of the car after 9 years.
g. Use your linear equation to approximate the price of the car after 15 years.
h. Use your equation to approximate the number of years until a car is worth $5,000.
i. Use your equation to approximate the number of years until a car is worth $16,000.
j. Do any of these answers not make sense? Explain.
k. Is a straight line a good model for this type of data?
10. Israel sees the graph on the left and is asked to draw a line to represent the data. His line is shown on
the right. Explain whether this line is a good line or not and why.
Math 95 – Homework Unit 4 – Page 7
11. Isabella sees the graph on the left and is asked to draw a line to represent the data. Her line is shown
on the right. Explain whether this line is a good line or not and why.
12. The graph below represents student grades on a quiz (out of 100) based on the number of hours of
cell-phone usage they had the day before the exam.
a. Draw a line that best represents the data. As the hours go up, the grade on the quiz is
(increasing/decreasing)?
b. Label each axis with the appropriate words and units.
c. Use the line to find the slope and y-intercept. Interpret each of them in the context of the graph.
d. Create a linear equation using the information you found in the previous part.
e. Use your linear equation to approximate the score on the quiz if a phone was used for 4 hours.
f. Use your linear equation to approximate the score on the quiz if a phone was used for 16 hours.
g. Use your linear equation to approximate the score on the quiz if a phone was used for 6 hours.
h. Use your linear equation to approximate the number of hours on the phone to get a score of 70.
i. Use your linear equation to approximate the number of hours on the phone to get a score of 40.
j. Is a straight line a good model for this type of data?
Math 95 – Homework Unit 4 – Page 8
13. The graph below represents the cost (in $) for a plumber to work a particular job (measured in
hours).
a. Draw a line that best represents the data. As the hours go up, the cost of the plumber is
(increasing/decreasing)?
b. Label each axis with the appropriate words and units.
c. Use the line to find the slope and y-intercept. Interpret each of them in the context of the graph.
d. Create a linear equation using the information you found in the previous part.
e. Use your linear equation to approximate the cost of a 6 hour job.
f. Use your linear equation to approximate the cost of a 1.25 hour job.
g. Use your linear equation to approximate the cost of a 20 hour job.
h. Use your linear equation to approximate the number of hours for a $100 bill.
i. Use your linear equation to approximate the number of hours for a $900 bill.
j. Use your linear equation to approximate the number of hours for a $275 bill.
k. Is a straight line a good model for this type of data?
Wrap-up and look back:
14. Would you expect a positive slope or negative slope when comparing hours worked (x-axis) with
total amount paid (y-axis)? Explain.
a. What would it mean if the slope was negative?
15. Would you expect a positive slope or negative slope when comparing hours worked (x-axis) with
percent of a job left to do (y-axis)? Explain.
a. What would it mean if the slope was positive?
16. Write in words what you learned from this section. Did you have any questions remaining that
weren’t covered in class? Write them out and bring them back to class.
Math 95 – Homework Unit 4 – Page 9
4.3 Basics of Statistics – Weighted Averages
Vocabulary and symbols – write out what the following mean:



Descriptive Statistics
Inferential Statistics
Median



Mean
Mode
Weighted average
Concept questions:
1. Is it possible that the mean could be more than the median? Explain how this could occur and give
an example set of data.
2. Is it possible that the mean could be less than the median? Explain how this could occur and give an
example set of data.
3. Podric is trying to find the median in the set of data: 10, 14, 16, 20. He says there is no “middle”
number so there is no median. Is he correct? Explain.
4. Brienne is trying to find the mode in the set of data: 10, 14, 16, 20. She says there is no “most”
number so there is no mode. Is she correct? Explain.
5. Bran is trying to find the mode in the set of data: 10, 14, 14, 16, 20, 20. He says there are 2 modes
because both 14 and 20 occur more than the others. He says it’s like a first place tie. Is he correct?
Explain.
6. Can a set of data have more than one mean? Can a set of data have more than one median? Can a set
of data have more than one mode? Explain.
7. Can a set of data have no mean? Can a set of data have no median? Can a set of data have no mode?
Explain.
8. If the mean of a group of 4 quizzes was 85 and the next quiz taken is a 90, does the mean go up or
down? Explain and find the new mean.
9. Will the mean, median, or mode be an actual number in the data set? Explain.
10. Carl and Daniel are debating medians. Carl says that he can think of a set of data that has a median
of 80, but when one more data value of 85 is added, the new median is smaller. Daniel says this can
never happen. Who is correct? If you say Carl, create a set of data to show your result. If you say
Daniel, explain why it could never happen.
11. Alice and Betty are debating modes. Alice says that she can think of a set of data that has a mode of
80, but when one more data value of 85 is added, the new data set has two modes. Betty says this can
never happen. Who is correct? If you say Alice, create a set of data to show your result. If you say
Betty, explain why it could never happen.
Math 95 – Homework Unit 4 – Page 10
Exercises:
12. Sometimes the mean is known as the “balancing point” for a set of data. This exercise will show
why it is called that.
a. Determine the mean of this set of data: 2, 3, 6, 8, 11.
b. For each number, find the “data value minus mean”; this is called the deviation. A number
below the mean will have a negative deviation and a number above the mean will have a positive
deviation. What is the deviation of a number that is equal to the mean? Why?
c. Add up all the deviations – what is the result?
13. If you know the mean of a set of data, can you find the sum of the data values?
a. x  28 , n = 5
c. x  61.2 , n = 57
b. x  137.5 , n = 58
d. x  37 , n = 23
14. If you know the sum of a set of data, can you find the mean of the data values?
a. x = 40, n = 10
c. x = 627, n = 75
b. x = 491, n = 25
d. x = 26.1, n = 30
15. Find the mean, median, and mode for each set of data. Calculator only, not a computer.
a. 5, 9, 13, 13, 2
c. 16, 20, 4, 1, 1
b. 11, 22, 95, 40, 38, 88
d. 7, 103, 7, 9, 28, 9, 33
16. Use your computer to find the mean, median, and mode for:
a. 12, 112, 214, 15, 18, 18, 19, 20, 21, 23, 11, 16, 18, 23, 31, 14, 20, 18, 12
b. 6, 8, 6, 8, 9, 6, 8, 6, 8, 9, 11, 5, 5, 5, 2, 4, 3, 3, 3, 4, 10
c. 237, 411, 298, 300, 302, 405, 299, 500, 7, 400, 377, 222, 233, 244, 255, 18
17. Find the mean score on the quiz:
6
Score on Quiz
8
Number of Students
7
28
8
45
9
17
10
14
18. Find the mean weight of the students:
85
Weight (in pounds)
8
Number of Students
90
7
95
12
100
20
105
28
19. If you have a test average (mean) of 75 after 4 tests, and then get a 90 on the next test, what is your
new mean?
20. In standard (00-wheel) roulette, what is the weighted average of:
a. a bet on a single number where the payouts are 35:1.
b. a bet on 4 numbers where the payouts are 8:1.
c. a bet on high (18 numbers) where the payouts are 1:1.
21. In European (0-wheel) roulette, what is the weighted average of:
a. a bet on a single number where the payouts are 35:1.
b. a bet on 4 numbers where the payouts are 8:1.
c. a bet on 2 numbers where the payouts are 17:1.
d. a bet on high (18 numbers) where the payouts are 1:1.
Math 95 – Homework Unit 4 – Page 11
22. In a math class, the students earn grades from different categories. Homework is worth 10%,
Quizzes are 20%, Exams are 40%, and the Final Exam is 30%.
a. Rachelle earns 80% on homework, 50% on quizzes, 60% on exams, and 70% on the final. What
is her overall grade?
b. Jordan earns 60% on homework, 70% on quizzes, 80% on exams, and 60% on the final. What is
his overall grade.
c. Jocelyn earns 80% on homework, 80% on quizzes, 80% on exams, and 80% on the final. What is
her overall grade?
d. Jackson earns 80% on homework, 80% on quizzes, 80% on exams, and 50% on the final. What
is his overall grade?
e. Penny earns 60% on homework, 60% on quizzes, 60% on exams, and 90% on the final. What is
her overall grade?
23. Calculate the GPA for the student below.
Class
Credits
Grade (letter)
Math
4
C
English
3
C
Chemistry
4
B
Yoga
1
A
Grade (points)
Quality Points
Grade (points)
Quality Points
Grade (points)
Quality Points
Totals
24. Calculate the GPA for the student below.
Class
Credits
Grade (letter)
Math
4
C
English
3
A
History
4
B
Sociology
4
A
Totals
25. Calculate the GPA for the student below.
Class
Credits
Grade (letter)
Media Arts
2
C
English
4
D
Chemistry
5
A
Spanish
4
C
Totals
Math 95 – Homework Unit 4 – Page 12
26. If your GPA is 3.81 after earning 160 quality points, and then you take one 4-unit class and get a D,
what will your new GPA be?
27. Yogi’s GPA was 2.13 after earning 100 quality points. He then took 16 units and earned a GPA of
3.5 on those units. What will his new cumulative GPA be?
28. In a class, exams are worth 60% and a project is worth 40%. What is the lowest exam average
possible to get 70% overall if a student earns 100% on the project?
29. In a class, exams are worth 60% and a project is worth 40%. What is the lowest project average
possible to get 70% overall if a student earns 100% on exams?
30. In a class, exams are worth 60% and a project is worth 40%. If a student earns 40% on exams, can
the student pass the class with a 70% overall? Explain.
31. In December 2000, Alex Rodriguez signed a contract guaranteeing him $252 million over 10 years,
which was $25.2 million per year. In the same year, the Minnesota Twins paid 26 players an average
of $635,365. If A-Rod was traded to the Twins, they would have 27 players… what would be their
new average salary?
32. In 1970, baseball had a minimum salary of $12,000 and an average salary of $29,303. In 1985, the
minimum salary was $60,000 and the average salary was $371,571.
http://www.stevetheump.com/Payrolls.htm
a. Consider a team in 1970 that had 26 players all making the minimum salary. If one person
making the average 1985 salary was added to that group, what would be the new average for the
team?
b. Consider a team in 1985 that had 26 players all making the minimum salary. If one person
making the average 1970 salary was added to that group, what would be the new average for the
team?
c. Consider a team in 1985 that had 26 players all making the average salary. If one person making
the average 1970 salary was added to that group, what would be the new average for the team?
d. When you have a large group of people at an average salary, will one person’s salary really
impact the average by that much? Explain your conclusion.
33. In 2016, on opening day the San Francisco Giants had a total player payroll of $166,495,942. The
mean salary for the team was $5,946,284 and the median was $4,000,000. The same year, the
Philadelphia Phillies had a total player payroll of $133,048,000. The mean salary for the team was
$4,434,933 and the median was $700,000.
a. How many players were on the roster for the Giants?
b. How many players were on the roster for the Phillies?
c. Based on the information, which team had more low paid players? Why?
d. Explain the differences between the mean and median for each team.
34. In 2016, the Houston Astros were the team with the lowest player payroll of $69,064,200. Their
mean salary was $2,466,579 and the median salary was $1,031,250.
a. Based on these numbers and the previous problem, would you rather play for the Astros or the
Phillies? Explain your answer.
b. How many people were on the roster for the Astros on opening day?
c. The league minimum salary was $507,500. Which team would you wager had more people close
to the league minimum? Why?
Math 95 – Homework Unit 4 – Page 13
Wrap-up and look back:
35. Interpret the meaning of the mode, meaning, and mean based on used car sales.
a. The mean is $11,855.
b. The median is $9,502.
c. The modes are $7,850 and $12,100.
36. If two students are taking the same 3 classes, and each student gets two “B” and one “A” grade, will
they each get the same GPA? Explain.
37. Write in words what you learned from this section. Did you have any questions remaining that
weren’t covered in class? Write them out and bring them back to class.
4.4: Likelihood Analysis
Vocabulary and symbols – write out what the following mean:

N/A
Concept questions:
1. If 67.5% of the data is below 48, what percent is greater than or equal to 48?
2. If 40% of the data is a 55 or lower, and 3% of the data is actually a 55, what percent of the data is lower
than 55?
3. If 68.8% of Americans are overweight or obese, and 35.7% of Americans are obese,
a. what percent of Americans are overweight?
b. what percent of Americans are not obese?
c. what percent of Americans are neither overweight nor obese?
d. what percent of Americans are not overweight?
4. With the coin examples in class, flipping a single coin 100 times led to a mean number of heads. What
was the mean number?
5. From the coin example, flipping a single coin 100 times led to a mode number of heads. What was the
mode?
6. From the coin example in the book, how many heads (out of 100 flips) would happen less than 20% of
the time? (there is a high number and a low number)
7. From the coin example in the book, how many heads coming up would you say would happen less than
30% of the time? (there is a high number and a low number)
8. From the coin example in the book, how many heads coming up would you say would happen less than
40% of the time? (there is a high number and a low number)
9. Intelligence is sometimes measured by using an IQ test. IQ is measured on a scale with a mean and
median of 100. What does it mean to have a median of 100?
Math 95 – Homework Unit 4 – Page 14
Exercises:
10. A chart showing IQ and percent of all people is shown below. Compute the cumulative percentages for
the open boxes.
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
0.1%
0.1%
0.1%
0.1%
0.1%
0.1%
0.2%
0.2%
0.2%
0.3%
0.3%
0.3%
0.4%
0.4%
0.5%
0.6%
0.6%
0.7%
0.8%
0.9%
1.0%
1.0%
1.1%
1.2%
1.3%
1.5%
1.6%
1.7%
1.8%
1.9%
2.0%
2.1%
2.2%
2.3%
2.3%
2.4%
2.5%
2.5%
2.6%
2.6%
2.6%
2.7%
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
2.7%
2.6%
2.6%
2.6%
2.5%
2.5%
2.4%
2.3%
2.3%
2.2%
2.1%
2.0%
1.9%
1.8%
1.7%
1.6%
1.5%
1.3%
1.2%
1.1%
1.0%
1.0%
0.9%
0.8%
0.7%
0.6%
0.6%
0.5%
0.4%
0.4%
0.3%
0.3%
0.3%
0.2%
0.2%
0.2%
0.1%
0.1%
0.1%
0.1%
0.1%
0.1%
Math 95 – Homework Unit 4 – Page 15
11. Using the distribution analysis for an IQ test, determine the answers to the following questions. Note
that for this table, all values form 58 to 143 are indicated with bars. The bar directly to the right of a tick
mark represents that IQ score.
a. At what two IQ scores would 0.5% of the population be located?
b. At what two IQ scores would about 2% of the population be located?
c. At what two IQ scores would about 1.6% of the population be located?
d. What is the most likely IQ score? Would you call this the mean, median, or mode?
e. Would you consider this picture to be symmetric?
f. About what percent of the population scores a 112?
g. About what percent of the population scores a 68?
h. About what percent of the population scores a 102?
i. Would you say that it is more likely that you find someone who scored a 106 on the IQ test or
someone who scored an 82? Explain.
j. Would you say that it is more likely that you find someone who scored a 142 on the IQ test or
someone who scored a 75? Explain.
k. How likely is it for someone to score a 150 on the IQ test? Explain.
Math 95 – Homework Unit 4 – Page 16
12. Using the cumulative distribution analysis for the IQ test, determine the answers to the following
questions.
a. 10% of the population scores at what IQ or lower?
b. 20% of the population scores at what IQ or lower?
c. 30% of the population scores at what IQ or lower?
d. 40% of the population scores at what IQ or lower?
e. 50% of the population scores at what IQ or lower?
f. 60% of the population scores at what IQ or lower?
g. 70% of the population scores at what IQ or lower?
h. 80% of the population scores at what IQ or lower?
i. 90% of the population scores at what IQ or lower?
j. 95% of the population scores at what IQ or lower?
k. 5% of the population scores at what IQ or lower?
l. Someone scoring a 130 on the IQ test would be rated higher or lower than most of the population?
m. In the movie Sneakers (1992), one of the doctors drove around in a vehicle with the custom license
place saying “180 IQ.” Based on our data, do you believe the person or think they are being
extremely cocky? Explain.
Math 95 – Homework Unit 4 – Page 17
13. Determine the values of the following based on the IQ test. Let X represent the score on the IQ test.
Answer these questions.
a. P X  100
e. P X  79
b. P X  85
f.
c. P X  115
g. P X  105
d. P X  90
h. P X  120
P X  110
14. If X represents the score on a quiz in Math 95, interpret the following:
a. P X  100  0.60
b. P X  100  0.03
c. Use the previous information to find and interpret P X  100 .
15. If X represents the weight of a female baby (in pounds) who is 2 years old, interpret the following:
a. P X  25  0.40
b. P X  33  0.23
c. P X  26.5  0.03
16. If X represents the weight of a male baby (in pounds) who is 2 years old, interpret the following:
a. P X  25  0.28
b. P X  33  0.36
c. P X  26.5  0.022
17. If X represents the height of a male American who is over 18 years old (in inches), interpret the
following:
a. P X  69  0.50
b. P X  84  0.03
c. P X  66  0.04
Wrap-up and look back:
18. Write in words what you learned from this section. Did you have any questions remaining that
weren’t covered in class? Write them out and bring them back to class.
4.5: Critical Thinking with Numbers – Simpson’s Paradox
Vocabulary and symbols – write out what the following mean:

Simpson’s Paradox
Concept questions:
1. If 44% of men who applied to a school were admitted and only 35% of women who applied were
admitted, is your gut instinct that there is a bias against women at the school? Explain.
2. If all groups have the same number of participants, and Drug M works better than Drug N, can
Simpson’s Paradox apply? Why or why not?
Math 95 – Homework Unit 4 – Page 18
3. If a medical study has two groups: Group A receives one drug and Group B receives another. Each
group is broken down into 2 smaller subgroups and the percentage of people who are cured by the drug
is calculated. Is it possible that both smaller subgroups of Group A are higher than the subgroups of
Group B, and Group A is higher overall than Group B? Give actual numbers to back up your claim.
4. If a medical study has two groups: Group A receives one drug and Group B receives another. Each
group is broken down into 2 smaller subgroups and the percentage of people who are cured by the drug
is calculated. Is it possible that both smaller subgroups of Group A are higher than the subgroups of
Group B, but Group B is higher overall than Group A? Give actual numbers to back up your claim.
5. If group A is higher in one case and group B is higher in another, is this an indication of Simpson’s
Paradox? Why or why not?
Exercises:
6. Consider Drug P and Drug Q, and their successes in different groups of people.
Drug P
% success
Drug Q
Group 1
66 out of 91
8 out of 10
Group 2
2 out of 9
23 out of 90
% success
Totals
a. Determine the %-success for each group and each drug.
b. Determine the totals if the groups are combined and the %-success for the drug overall.
c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.
7. Consider Drug P and Drug Q, and their successes in different groups of people.
Drug P
% success
Drug Q
Group 1
66 out of 91
8 out of 10
Group 2
8 out of 9
22 out of 90
% success
Totals
a. Determine the %-success for each group and each drug.
b. Determine the totals if the groups are combined and the %-success for the drug overall.
c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.
Math 95 – Homework Unit 4 – Page 19
8. Consider Drug P and Drug Q, and their successes in different groups of people.
Drug P
% success
Drug Q
Group 1
66 out of 91
61 out of 91
Group 2
8 out of 9
2 out of 9
% success
Totals
a. Determine the %-success for each group and each drug.
b. Determine the totals if the groups are combined and the %-success for the drug overall.
c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.
9. Consider Drug P and Drug Q, and their successes in different groups of people.
Drug P
% success
Drug Q
Group 1
75 out of 125
83 out of 125
Group 2
98 out of 125
112 out of 125
% success
Totals
a. Determine the %-success for each group and each drug.
b. Determine the totals if the groups are combined and the %-success for the drug overall.
c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.
Wrap-up and look back:
10. If Jim saved more money than Stanley on day 1, and Jim saved more money than Stanley on day 2, if
you combined the savings, who would have more savings? Explain.
11. Is the previous question an example of Simpson’s Paradox? Why or why not?
12. Why is Simpson’s Paradox considered a “paradox”? What does the word paradox mean?
13. In life, is it enough to ‘feel’ that something should be a certain way, or do we need more to show the
results?
14. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
Math 95 – Homework Unit 4 – Page 20
4.6: Wrap-up and Review
Key concepts in the courses:
 Gaining an appreciation for number sense
 Solving linear equations
 Graphing lines and using slope and intercept to interpret the relationships between input and output
 Likelihood and probability
 Expected values and weighted averages
 Relationships using Venn diagrams
 Understanding conditional statements and using correct reasoning for arguments
 Financial awareness and the basics of investing, borrowing, and saving for retirement
 A clear understanding of the time-value of money
 Using tables, charts, graphs, and formulas to solve problems
 Being comfortable with a computer for data entry (and financial predictions)
 Through repeated problem types, seeing that there is often more than one way to solve a problem
 Gaining more confidence in computation, interpretation, and understanding the concepts and
usefulness of mathematics
We end with some quotes from Henry Ford that seem very fitting to this course and your futures.





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Whether you think you can or you think you can’t, you’re right.
Anyone who stops learning is old, whether at 20 or 80. Anyone who keeps learning stays young.
Thinking is the hardest work there is, which is probably the reason so few engage in it.
The only real mistake is the one from which we learn nothing.
Failure is only the opportunity more intelligently to begin again.
Obstacles are those frightful things you see when you take your eyes off your goals.
Keep your goals in mind and remember that math is a tool to help you reach them, not a hurdle to be
hopped over and forgotten about. Be positive and push through; learn from your mistakes and constantly
look to improve. We have faith in you because you CAN do this!
Math 95 – Homework Unit 4 – Page 21