Download Key - Clemson Mathematical Sciences

STAT 3090
Test 1 - Version A
Fall 2015
Student’s Printed Name: ____________________________
XID:___________________
Instructor: ________________________________
Section # :_________
Read each question very carefully. You are permitted to use a calculator on all portions of this exam. You are NOT
allowed to use any textbook, notes, cellphone, or laptop on either portion of the exam. No part of this exam may be
removed from the examination room.
In order to receive full credit for the free response portion of the exam, you must:
1. Show legible and logical (relevant) justification which supports your final answer.
2. Use complete and correct mathematical notation.
3. Include proper units, if necessary.
You have 1 hour 30 minutes to complete the entire exam.
On my honor, I have neither given nor received inappropriate or unauthorized information during this exam.
Student’s Signature: _______________________________________________________________________
Do not write below this line.
Free Response
Problem
Possible
Points
1
4
2
4
3
4
4
4
5
4
6
4
7
8
8
8
9
8
10
1
Free Response
49
Multiple Choice
51
Test Total
100
Points
Earned
STAT 3090
Test 1 - Version A
Fall 2015
Multiple Choice: (Questions 1 - 17) Answer the following questions on the scantron provided using a #2 pencil.
Bubble the response that best answers the question. Each multiple choice correct response is worth 3 points. For
your record, also circle your choice on your exam since the scantron will not be returned to you. Only the
responses recorded on your scantron will be graded.
1.
Determine whether the given description corresponds to an observational study or an experiment.
In research sponsored by Coca-Cola, 12,500 people were asked what contributes most to their
happiness, and 77% of the respondents said that it was their family or partner.
A) Observational study
B) Controlled Experiment
2.
A college administrator is interested in the proportion of undergraduate students that wear orange on
Fridays at her college. A random sample of 68 undergraduates was taken (on a Friday) and the
number of them that were wearing orange was recorded. Which of the following is the population of
interest for this study?
A)
B)
C)
D)
3.
Which of the following is the best description of standard deviation?
A)
B)
C)
D)
4.
All undergraduate students at the college
The number of undergraduate students that wear orange on Fridays at the college
The 68 undergraduates that were polled.
The proportion of undergraduates that wear orange on Fridays at the college
A measure of the typical deviation between the mean and median
A measure of the typical deviation between two data points
A measure of the typical deviation a data point is from the mean
A measure of the typical squared deviation from the mean
If you roll two dice which of the following is true?
A) It is more likely to roll a 4, 3 than to roll a 4, 4
B) It is more likely to roll a 4, 4 than to roll a 4, 3
C) There is an equal chance of rolling a 4, 3 or a 4, 4
5.
If event A and B are mutually exclusive, which of the following must be true?
A)
B)
C)
D)
P(A or B) = 0
P(A and B) = 0
P(A |B) = 0
P(A and B) = P(A) ∙ P(B)
1
STAT 3090
6.
Test 1
Test 2
She did equally well on both tests
Cannot determine from the information given
The following statement is an illustration of what type of statistic?
“Based on a sample of 500 registered republicans we predict that Donald Trump will win the South
Carolina primary by between 35 to 37% of the vote”
A)
B)
C)
D)
8.
Fall 2015
Holly is taking a psychology class. On the first test the class average was 85 and the standard
deviation was 6. On the second test the class average was 75 and the standard deviation was 4.
Holly scored a 79 on the first test and a 73 on the second test. Which test did she perform better on
relative to the rest of her class?
A)
B)
C)
D)
7.
Test 1 - Version A
Descriptive Statistic
Inferential Statistic
Nominal Statistic
Ordinal Statistic
Which of the following best describes the shape of the distribution of the following data?
Stem Plot of average number of sit ups for middle schoolers, Key: 1|1 = 1.1
Stem
1
2
3
4
5
6
7
8
A)
B)
C)
D)
Leaf
1123344
5668
03
78
5788
00012444
556777889
Skewed left
Skewed right
Symmetric and mound (bell) shaped
Symmetric and non-mound shaped
2
STAT 3090
9.
Test 1 - Version A
Fall 2015
Below is a boxplot of the weights of 44 high school football players.
What percentage of the data is between 164 and 191?
A)
B)
C)
D)
Approximately 61%
Approximately 25%
Approximately 28%
Approximately 27%
10. The number of hours per week that the television is turned on is determined for each family in a
sample. The mean of the data is 32 hours and the median is 28.2 hours. Twenty-four of the families
in the sample turned on the television for 17 hours or less for the week. The 11th percentile of the
data is 17 hours. Based on the given information, which of the following do you know is true?
A)
B)
C)
D)
The 60st percentile is less than 32 hours
The 57th percentile is greater than or equal to 27 hours
There are 200 families in the sample
24 families in the sample turned on the television between 17 hours and 28.2 hours
11. Below is a dataset of speed of tennis serves (in mph) for women’s tennis. If you were to create a
boxplot of the data which (if any) of the values would be classified as outliers?
78
A)
B)
C)
D)
95
110
114
116
117
120
120
121
122 128
128
78
Both 128 and 78
There are no outliers for this data
3
STAT 3090
Test 1 - Version A
Fall 2015
12. The following histograms represent test scores for 4 different tests in Statistics. Which of the tests
had the largest variability in scores.
Frequency
Frequency
10
10
0
0
6
7
8
9
10
11
12
13
6
14
Test 3
7
8
9
10
11
12
10
0
13
14
Test 4
20
Frequency
20
Frequency
Test 2
20
Test 1
20
10
0
6
A)
B)
C)
D)
7
8
9
10
11
12
13
14
6
7
8
9
10
11
12
13
14
Test 1
Test 2
Test 3
Test 4
4
STAT 3090
Test 1 - Version A
Fall 2015
13. A group of 15 adult females are training to run/walk a 5k as a team. For their first 5k run together the
summary statistics were as follows:
Median = 36 minutes
Mean = 30 minutes
Standard Deviation = 3 minutes
After a month of training each of their individual times decreased by exactly 2 minutes. What is the
groups mean and standard deviation after a month of training?
A)
B)
C)
D)
E)
Median = 36 minutes; Mean = 30 minutes; Standard Deviation = 3 minutes
Median = 34 minutes; Mean = 28 minutes; Standard Deviation = 1 minute
Median = 38 minutes; Mean = 32 minutes; Standard Deviation = 5 minutes
Median = 34 minutes; Mean = 28 minutes; Standard Deviation = 3 minutes
Cannot determine from the information given
14. Below is a table that summarizes the number of fatal shark attacks per state in the US from 1837 –
2014.
State
Florida
California
South Carolina
North Carolina
Texas
New Jersey
Virginia
Massachusetts
Number of
attacks
11
10
2
3
2
5
1
1
What is the relative frequency for the number of fatal shark attacks in South Carolina?
A)
B)
C)
D)
2
2/35
3/35
1/8
15. Classify the following variable as either Quantitative, Qualitative or Neither:
Price of a textbook
A) Quantitative
B) Qualitative
C) Neither
5
STAT 3090
Test 1 - Version A
Fall 2015
16. Determine whether the given value is a statistic or a parameter:
The average (mean) atomic weight of all elements in the periodic table is 134.355 unified atomic
mass units.
A) Parameter
B) Statistic
17. Below is a stacked bar chart of data on fruit consumption from three different individuals. How
many Bananas does Jane consume?
A)
B)
C)
D)
1
2
3
8
6
STAT 3090
Test 1 – Fall 2015
Version A
1. At Six Flags in Atlanta, GA a college student randomly selected 7 park guests and recorded the number
of times the individuals rode the Superman: Ultimate Flight ride. The following were the recorded
results:
3 5 4 7 3 2 4
Calculate the standard deviation of the number of times the individuals rode the Superman ride. Provide the
correct notation (symbol) and your value to 3 decimal places in the blanks provided below. You must show
ALL work for credit. (Calculator jargon will not be counted as work shown).
𝑥𝑥̅ =
𝒙𝒙
3
5
4
7
3
2
4
28
28
=4
7
�
𝒙𝒙 − 𝒙𝒙
3 – 4 = -1
5–4=1
4–4=0
7–4=3
3 – 4 = -1
2 – 4 = -2
4–4=0
0
𝑠𝑠 2 =
s
(𝒙𝒙 − 𝒙𝒙
�)𝟐𝟐
1
1
0
9
1
4
0
16
16
= 2.66667
7−1
𝑠𝑠 = √2.66667 = 1.633
1.633______________
___________ _____________ = __________
rides
Grading:
Points Earned
4
2
0
Logic
Has notation (symbol) and value correct with work shown
Has either notation (symbol) OR value correct with work shown but not both
Neither notation or value is correct
Notes: There will be some students that calculate variance correctly and forget to take the square root for
standard deviation these students will receive no credit for this problem. Think of the fill in the blank questions
as glorified multiple choice questions if this question would have been asked in multiple choice format the
value of variance would have been one of the choices and would be marked completely incorrect. In the case
where a student does not take the square root it is difficult for us (the graders) to determine if this student “just
forgot” to take the square root or legitimately thinks that s2 is standard deviation. In either case it is not
answering the question that is asked of the student.
STAT 3090
Test 1 – Fall 2015
Version A
2. A histogram of the weights of US dimes is mound (bell) shaped and symmetric with a mean of 2.3
grams and a standard deviation of 0.04 grams. Approximately what percentage of dimes have weights
between 2.26 and 2.38 grams? Write answer in blank provided below.
0.04
= −1
𝑧𝑧2 =
2.38−2.3
0.04
=2
95% / 2 = 47.5%
2.26−2.3
68 % / 2 = 34%
𝑧𝑧1 =
Approximately 34% of dimes are within mean and 1 standard deviation below the mean.
Approximately 47.5% of dimes are within mean and 2 standard deviations above the mean.
_____________
81.5%________________
Grading:
Points Earned
4
0
Logic
Value is correct in decimal or percent form (with or without percent sign) with some
work shown
[Work could include (but not limited to) calculation of z-scores, adding up 34 + 47.5,
or calculating 34 as half of 68%. Some logical explanation of where the number
came from.]
Value is incorrect or value correct with NO work shown
STAT 3090
Test 1 – Fall 2015
Version A
In the judicial case of United States v. City of Chicago, discrimination was charged in a qualifying exam for the
position of Fire Captain. In the table below, Group A is a minority group and Group B is a majority group.
Group A
Group B
Total
Passed
10
417
427
Failed
14
145
159
Total
24
562
586
3. Find the probability of randomly selecting one of the test subjects who is in Group A or passed. Write
the correct probability notation/statement (i.e., P(…)), work shown, and value to 4 decimal places in the
blanks provided below.
A = event subject is in group A
P = event subject passed the exam
P(A or P)
(427+24-10)/586=
_________
___________ = __
(Probability Statement)
(work shown)
0.7526
________
_________
(value to 4 decimal places)
Grading:
Points Earned
4
2
0
Logic
Has notation and value correct with work shown
Has either notation OR value correct with work shown but not both
Neither notation or value is correct
Note: Notation for this problem should include explanation of any short-hand notation (for example if the
student uses a probability statement P(A or B) they must indicate what event A and B represent). However, if
no short-hand notation is used that is acceptable (for example P(Group A or passed)). The short-hand notation
of A and P are acceptable without explanation as it is clear from the problem what is meant by A and P.
STAT 3090
Test 1 – Fall 2015
Version A
In the judicial case of United States v. City of Chicago, discrimination was charged in a qualifying exam for the
position of Fire Captain. In the table below, Group A is a minority group and Group B is a majority group.
Group A
Group B
Total
Passed
10
417
427
Failed
14
145
159
Total
24
562
586
4. Find the probability of randomly selecting one of the test subjects who is in Group B and passed the
exam. Write the correct probability notation/statement (i.e., P(…)), work shown, and value to 4 decimal
places in the blanks provided below.
B = event subject is in group B
P = event subject passed the exam
417/586______ =
_______P(B and P)_______ = _____
(Probability Statement)
(work shown)
_____0.7116_______
(value to 4 decimal places)
Grading:
Points Earned
4
2
0
Logic
Has notation and value correct with work shown
Has either notation OR value correct with work shown but not both
Neither notation or value is correct
Note: Notation for this problem should include explanation of any short-hand notation (for example if the
student uses a probability statement P(A and B) they must indicate what event A and B represent). However, if
no short-hand notation is used that is acceptable (for example P(Group B and passed)). The definition of shorthand notation can be found anywhere on the page (for example if a student defines P in Question 3 and uses it
again for Question 4 that is acceptable). The short-hand notation of B and P are acceptable without explanation
as it is clear from the problem what is meant by B and P.
STAT 3090
Test 1 – Fall 2015
Version A
5. The employees at a large university were classified according to age as well as to whether they belonged
to administration, faculty, or staff. For all probabilities give three decimal places.
Administration
Faculty
Staff
Total
Age Group
31-40 41-50
51 or Over
24
16
17
40
36
28
20
14
2
84
66
47
20-30
2
1
16
19
Total
59
105
52
216
Let A = the event a randomly selected employee is a staff member
Let B = the event a randomly selected employee is 31 - 40 years old.
Are the events A and B independent? Justify your answer using probabilities.
This problem can be answered in a couple of different ways. There are 3 ways that are most popular,
those solutions are shown here …
(1) 𝑃𝑃(𝐴𝐴) =
(2) 𝑃𝑃(𝐵𝐵) =
52
216
84
216
= 0.2407 𝑃𝑃(𝐴𝐴|𝐵𝐵) =
= 0.3889 𝑃𝑃(𝐵𝐵|𝐴𝐴) =
(3) 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵) =
52 84
216 216
are independent
20
84
20
52
= 0.2381 Since P(A) ≈ P(A|B) then A and B are independent
= 0.3846 Since P(B) ≈ P(B|A) then A and B are independent
= 0.0936 𝑃𝑃(𝐴𝐴 𝑎𝑎𝑎𝑎𝑎𝑎 𝐵𝐵) =
20
216
= 0.0926 Since P(A)P(B) ≈P(A and B) then A and B
Grading:
Points Earned
4
2
0
Logic
Calculates correct probabilities AND ties those calculations to decision of independence
Calculates correct probabilities but does not directly tie those calculations to the decision
of independence. (for example P(A) = 0.2407 P(A|B) = 0.2381 independent – student
must indicate that because probabilities are equal that implies independence)
otherwise
Note: If a student suggests that 0.2407 is not equal to 0.2381 and therefore A and B are dependent that IS
ACCEPTABLE as long as they have clearly indicated that the two probabilities are not equal (this would
also be true for version (2) and version (3))
STAT 3090
Test 1 – Fall 2015
Version A
6. The National Governors Association publishes data on U.S. governors in Governors’ Political
Affiliations & Terms of Office. Based on that document, we obtained the following frequency
distribution for U.S. governors, as of 2010.
Party
Frequency
Democratic
26
Republican
24
Two U.S. governors are selected at random without replacement. What is the probability that the two
governors selected have different political-party affiliations? Provide the appropriate probability
notation/statement (i.e., P(…)), work shown, and value to 4 decimal places.
D = event governor is a democrat
R = event governor is republican
𝑃𝑃(𝐷𝐷𝐷𝐷) + 𝑃𝑃(𝑅𝑅𝑅𝑅) =
26 24 24 26
∙
+
∙
= 0.5094
50 49 50 49
Grading:
Points Earned
4
3
2
1
0
Logic
Has notation and value correct with work shown
Calculated both terms but did not add together
Has either notation OR value correct with work shown but not both
Imply understanding of without replacement but nothing else correct
Neither notation or value is correct
Note: Notation for this problem should include explanation of any short-hand notation (for example if the
student uses a probability statement P(A and B) they must indicate what event A and B represent). However, if
no short-hand notation is used that is acceptable (for example P(Democrat and Republican)). The short-hand
notation of D and Rare acceptable without explanation as it is clear from the problem what is meant by D and R.
STAT 3090
Test 1 – Fall 2015
Version A
7. The following is a stem and leaf plot of ages of a random sample of church members.
0|8
1|1 7 8
2|0
3|1 2 3 4 4 5 6 7 9 9
4|0 2 3
5|0
6|
7|5
Key: 1|1 = 11
a) (4 pts) Find the five number summary for the data above
Min = 8; Q1 = 25.5; Median = 34.5; Q3 = 39.5; Max = 75
Grading: 0.5 point for Minimum, 1 point for Q1, 1 point for Median, 1 point for Q3, 0.5 point for Max
b) (4 pts) Below is the boxplot of the data. Identify the values at each of the locations indicated below
A
B
C
The value at A = ______8_________
The value at B = _______25.5______
The value at C = ______50_______
The value at D = ______75_______
Grading = 1point for each blank (based on answers to part a)
D
STAT 3090
Test 1 – Fall 2015
Version A
8. The following histogram represents the number of cars per household for a sample of 40 US households.
20
18
18
Number of households
16
14
12
12
10
8
6
4
4
3
2
2
1
0
0
1
2
3
4
5
Number of Cars
A) (4 pts) Find the mean number of cars per household based on this data. Show work.
Grading:
𝑥𝑥̅ =
4(0) + 18(1) + 12(2) + 3(3) + 2(4) + 1(5)
= 1.6 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(4 + 18 + 12 + 3 + 2 + 1)
Points Earned
Logic
4
Has notation and value correct with work shown
3
Value correct with no notation OR value incorrect with minor arithmetic error
2
value correct with incorrect or no work shown
0
Neither notation or value is correct
Note: -0.5 for no units for the entire question
B) (4 pts) Find the median number of cars per household based on this data.
Location of Median: (0.5)(40) = 20  Median is located between the 20th and 21st numbers
Both the 20th and 21st numbers are 1’s. Therefore Median = 1
Grading:
Points Earned
4
3
Logic
Has notation and value correct OR value correct with work shown
Notation missing or no indication of work
Note: Work shown is some indication of how they determined where the median is located.
STAT 3090
Test 1 – Fall 2015
Version A
9. Some cruise ship passengers wear magnetic bracelets, which they (the passengers) say diminish the
effects of motion sickness. The on-ship medical clinic notes the number of passengers wearing bracelets
who complain of motion sickness compared to those who complain but are not wearing bracelets.
A) (4 pts) Does the above situation describe an observation or an experiment? Why?
Answers will varyModel Solution: This situation describes an observational study because the clinic is only
observing whether or not passengers are wearing the bracelets as opposed to imposing the
treatment of wearing the bracelet upon the passengers (as would be the case in an
experiment).
Grading:
Points Earned
4
2
2
0
Logic
Indicates situation is an observation and clearly explains why (there was no random
assignment of treatment or treatments were not imposed on subjects)
Claims experiment and gives good explanation clearly indicating an understanding of
experiment but not recognizing that it is not stated in the situation that the bracelets were
administered.
Indicates situation is observation but does not clearly explain why (for example never
says an incorrect statement but does not articulate clearly the reasoning)
Otherwise
B) (4 pts) Identify the two variables in this situation, determine whether the variable is the
explanatory or response; qualitative or quantitative; and discrete, continuous or neither.
Variables
Whether or not passenger wore a
bracelet
Whether or not passenger got
motion sick
Explanatory or Response
Explanatory
Response
Qualitative or Quantitative
Qualitative
Qualitative
Discrete, Continuous, or
Neither
Neither
neither
Grading: 0.5 points each – students must be consistent with their answers. For example, defining a variable as
“bracelet/no bracelet” is not a quantitative variable. However, a student that states the variable as “number of bracelets
worn” (although this is the statistic not the variable for this situation as the scenario was only performed once) should
claim their variable to be quantitative.