Test 1 – Version A
STAT 3090
Spring 2017
Multiple Choice: (Questions 1 – 20) 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.
The following bar chart shows the film rating for 140 randomly selected films at local theaters.
What is the relative frequency of the films rated “G”?
A. 12
B. 0.09
C. 0.19
D. 0.27
2.
A campus survey at Clemson University found that 72% of those surveyed bought a national
championship t-shirt. The number 72% is an example of a:
A. population
B. sample
C. parameter
D. statistic
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Test 1 – Version A
3.
STAT 3090
Spring 2017
In a survey of 1300 American high school students, 32% of the respondents reported that
someone had bullied them in school. What was the target population of this survey?
A. only the American high schools where bullying takes place
B. the collection of 1300 high school students
C. the collection of all American high school students
D. the collection of American high schools with police officers
4.
On Test 1, Devin computes his z-score using his test score, the mean test score and standard
deviation. How should Devin interpret his z-score of 2?
A. Devin scored 2 points above the mean score.
B. Devin’s score is twice the mean score.
C. Devin’s score is two standard deviations above the mean score.
D. Devin’s score is one-half the mean score.
5.
Which of the following best describes type and level of the following variable?
the number of courses in which a Clemson student is currently enrolled
A. discrete, ratio
B. discrete, ordinal
C. continuous, interval
D. discrete, interval
6.
What percentage of data points in a data set are greater than the 38th percentile value?
A. 38%
B. 62%
C. 72%
D. cannot be determined
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Test 1 – Version A
7.
STAT 3090
Spring 2017
The following histogram shows the Verbal SAT scores for 205 students entering a local college in
the fall of 2016.
The median score for these 205 students is:
A. about 40 or 41
B. between 19 and 26
C. between 400 and 500
D. between 500 and 600
8.
A survey collects many variables of interest about the competitors at the 2014 Winter Olympics.
Which of the following variables is qualitative?
A. country of origin
B. age of the athlete
C. time spent traveling to the venue
D. resting pulse rate of the athlete
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Test 1 – Version A
9.
STAT 3090
Spring 2017
Andrew decides to go on a fishing adventure. He records the number of catches per day for 10
days and creates the following dot plot to illustrate his results. Which of the following statements
is NOT true?
A. He caught fewer than 5 fish on 5 days.
B. Q1 = 1
C. The maximum number of fish that he caught was 20.
D. The median number of fish that he caught was 15.
10. A data set comprised of 1000 measurements is bell-shaped with mean 142 kg. If 95% of the data
lies between 99 kg and 185 kg, what is the standard deviation of these measurements?
A. 21.5 kg
B. 42 kg2
C. 14.3 kg
D. 42 kg
11. The monthly average number of phone calls to a local police station is 1022 with standard
deviation 130. State the range in which 75% of the phone calls will reside.
A. 632 to 1412
B. 762 to 1282
C. 892 to 1152
D. 957 to 1087
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Test 1 – Version A
STAT 3090
Spring 2017
12. A study conducted by the Defenders of Wildlife examined the typical mercury concentration in
cans of tuna sold in stores. The Defenders collected a sample consisting of 20 cans of albacore
tuna and 144 cans of light tuna from stores across the United States. The boxplots below
summarize the mercury concentrations found in the sampled cans (in parts per million, ppm).
What is the approximate value of the interquartile range of the distribution of mercury
concentrations found in the sampled cans of light tuna?
A. 0.15 ppm
B. 0.30 ppm
C. 0.80 ppm
D. 1.50 ppm
13. Based upon the boxplots in the previous question, which of the following statements is justified?
(A) Light tuna tends to have a lower mercury concentration than albacore tuna. And, light
tuna has less variability in mercury concentration than does albacore tuna.
(B) Light tuna tends to have a lower mercury concentration than albacore tuna. But, light tuna
has more variability in mercury concentration than does albacore tuna.
(C) Light tuna tends to have a higher mercury concentration than albacore tuna. But, light
tuna has less variability in mercury concentration than does albacore tuna.
(D) Light tuna tends to have a higher mercury concentration than albacore tuna. And, light
tuna has more variability in mercury concentration than does albacore tuna.
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Test 1 – Version A
STAT 3090
Spring 2017
14. The following boxplot shows the distribution of scores on the first exam in a calculus class.
Which of the following is true?
A. The mean score is less than the median score.
B. The mean score is greater than the median score.
C. The mean score is equal to the median score.
D. We cannot compare the mean and median score in this distribution.
15. It was reported by the South Carolina Cattle Association that the weights yearling steers are
symmetric and bell-shaped with a mean of 1152 pounds and standard deviation 84 pounds.
Approximately what percent of steers weigh more than 1,068 pounds?
A. 2.5%
B. 16%
C. 32%
D. 84%
16. If you toss two fair coins, what is the probability that one coin will land heads side up and the
other will land tails side up?
A. 1/4
B. 1/2
C. 2/3
D. ¾
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Test 1 – Version A
17
STAT 3090
Spring 2017
Of the following dot plots, which represents the set of data that has the largest standard deviation?
(A)
(B)
(C)
18. Recent data indicates that 11% of American men have high blood pressure AND high cholesterol.
If 32% of American men have high cholesterol, what percent of American men will have high
blood pressure GIVEN that they have high cholesterol?
A. 4%
B. 32%
C. 34%
D. 43%
19. Suppose that the probability that a U.S. resident has traveled to Canada is 0.17, to Mexico is 0.09
and to both countries is 0.04. What is the probability that an American chosen at random has
traveled to Canada or Mexico?
A. 0.16
B. 0.22
C. 0.26
D. 0.30
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Test 1 – Version A
STAT 3090
Spring 2017
20. A group of Clemson students are asked whether they carry an ATM card. The results are
summarized in the following table.
Freshman
Sophomore
Junior
Senior
Total
Carry ATM Does not Carry ATM Total
12
18
30
22
38
60
10
5
15
8
1
9
52
62
114
What is the probability that a randomly selected student is a Sophomore OR carries an ATM
card?
A. 0.98
B. 0.79
C. 0.92
D. 0.37
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Test 1 – Version A
STAT 3090
Spring 2017
Free Response: The Free Response questions will count as 40% of your total grade. Read
each question carefully. In order to receive full credit you must show logical (relevant)
justification which supports your final answer. You MUST show your work. Answers
with no justification will receive no credit.
1. The following data are the heights (in feet) of the 37 waterfalls in Greenville County
described in the book Waterfall Hikes of Upstate South Carolina (King, 2008), listed in
ascending order:
8
10
10
10
12
12
12
15
15
15
15
15
15
15
25
25
28
30
40
40
50
50
50
70
75
80
80
100 120 125 140 150
A.
18
20
20
Create a stem-and-leaf plot of this distribution. (4 pts)
Stem-and-leaf of Waterfall Height (ft)
Leaf Unit = 1.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
18
N
= 37
8
000222555555588
000558
0
00
000
05
00
0
05
0
0
1 pt for title and key (or statement of leaf unit)
No credit for graph (minus 3) if stems with no leaves are omitted.
No deductions for minor omission of a leaf.
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20
Test 1 – Version A
B.
STAT 3090
Spring 2017
Find the height that corresponds to the 60th percentile value for these data. Show your
calculation. (2 pts)
FORM A
0.60(37) = 22.2 - > round up to 23 - take the 23rd element
30 feet is the 60th percentile value
1 pt for correctly identifying which element correctly
1 pt for choosing correct element - no partial credit here if incorrect element
is chosen
C.
Write a few sentences describing center, shape and spread of the distribution of these
waterfall heights. Be sure to include appropriate summary measures for center and
spread. (4 pts)
The distribution of waterfall heights is skewed right (or skewed high), with center at a
median value of 20 feet. The interquartile range of heights is 45 feet.
1 pt – correct shape
1 pt – correct median as center
1 pt – variability as IQR – this should be IQR as there are outliers on the
upper end of the distribution
1 pt for context – should use the words “waterfall heights” or similar
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Test 1 – Version A
2.
Spring 2017
The following table displays the results of a survey about the use of technology by adults
over the age of 60 in South Carolina. Your responses may be unreduced fractions. If
you provide decimal responses, round to four decimal places.
Use Text Messaging
(T)
Does Not Use Text
Messaging
(not T)
Total
A.
STAT 3090
Use Email
(E)
148
Does Not Use Email
(not E)
25
Total
21
14
35
169
39
208
173
What is the probability that a randomly selected respondent uses email and uses text
messaging? (2 points)
P(E and T) = P(E ∩ 𝑻)= 148/208 ~ 0.7115
Deduct 0.5 points for improper notation. Deduct 0.5 pts for rounding errors
B.
Are using email and using text messaging mutually exclusive? Justify with probability.
(2 points)
No, because P(E ∩ 𝑻) is not equal to zero.
1 pt for correct decision, 1 pt for correct justification related to the
intersection of T and E
C.
What is the probability that a randomly selected respondent uses text messaging given
that they use email? (2 points)
P(T|E) = 148/169~0.8757
Deduct ½ pt for improper notation, deduct 2 points if condition is reversed
D.
Are using email and using text messaging independent? Justify with probability.
(4 points)
1 point for correct decision – 1 pt for correct notation – 2 points for correct
probabilities
Deduct 4 points for incorrect probabilities
P(T|E) = 148/169~0.8757 P(T)=173/208~ 0.8317
Since P(T|E) is not equal to P(T), these events are not independent.
OR P(E|T)= 148/173~0.8555 P(E)=169/208~0.8125 P(E|T) not = P(E)
OR P(E and T)=148/208 is not equal to P(E)P(T)=169/208(173)(208)
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Test 1 – Version A
3.
STAT 3090
Spring 2017
Your body's immune system protects you from disease and infection. If you have an
autoimmune disease, your immune system attacks healthy cells in your body.
A local newspaper published an article with the following headline.
Study Finds Strong Association Between Smoking and Autoimmune Disease
The article reported that a study tracked the medical histories of 15,016 men and women
for 17 years. The article stated that for those who smoked at least two packs of cigarettes
a day, the risk of autoimmune disease was 2.4 times the risk for those who did not smoke
or smoked less than two packs per day.
A. Identify the explanatory and response variables in the study. (2 points)
Explanatory variable: smoking at least two packs per day (-1/2 pt for just smoking)
Response variable: incidence of autoimmune disease
1 pt each. No credit if variables are reversed.
B. Is the study described in the article an observational study or an experiment? Explain.
(3 points)
Observational – there is no treatment imposed upon the subjects, subjects are not being
manipulated in any way, we are just observing.
1 pt for choosing observational – 2 pts explanation
No credit for choosing experiment.
C. Exercise status (regular weekly exercise versus no regular weekly exercise) was
mentioned as a possible confounding variable. Explain how exercise could be a
confounding variable in the study. (3 points)
Since this was an observational study, outside factors were not controlled. Subjects who
tended not to smoke (or smoke less) may have healthier habits including exercise. The
incidence of autoimmune disease could be affected by exercise rather than smoking.
1 pt for linking exercise to not smoking
1 pt for linking exercise to autoimmune disease
Subtract 3 if the student makes no attempt to link exercise to either variable.
12
Test 1 – Version A
STAT 3090
Spring 2017
4. Two companies, X and Y, hire many new college graduates as managers at entry-level
positions. In 2010, the starting salary for an entry-level manager was $36,000 per year at both
companies. At each company, data were collected from 20 employees who were hired in 2010
as entry-level managers who were still employed 5 years later.
The lower quartile, median, and upper quartile for the salaries of the sample of 20 employees at
Company X are shown in the table below, along with all values below the lower quartile and all
values above the upper quartile. The values are given in 1,000s.
Values Below Q1 Q1 Median Q3
Values Above Q3
$50
$55 $59, $59 61, $70, 80
Company X $36, $38, $39, 39 $47
A.
Determine if there are outliers in the company X salary distribution. Justify your response
clearly. (3 points)
1 pt upper fence: 55 + 1.5(8) = $67
1 pt lower fence: 47 – 1.5(8) = $35
$70, $80 are outliers because they are greater than the upper fence
1 PT each part: lower, upper, identify outliers
C.
The boxplot of the 20 salaries for Company Y is shown below. Construct the boxplot for
the Company X salaries on this same scale. (4 points)
1 pt for outliers, 1 pt for right whisker, 2 pts remainder of graph
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Test 1 – Version A
D.
STAT 3090
Spring 2017
Based upon the boxplots, give one reason why you might choose to accept a job at
Company X. (2 points)
Student must use choose an attribute of the graph of the salaries for Company X and
compare that attribute to the Company Y distribution.
1 pt for choosing the attribute, 1 pt for comparison to Y
Example: The maximum salary for Company X is greater than Company Y.
E.
Based upon the boxplots, give one reason why you might choose to accept a job at
Company Y. (2 points)
Student must use choose an attribute of the graph of the salaries for Company Y and
compare that attribute to the Company X distribution.
Example: Company Y has a higher min, Q1 and median salary than Company X.
1 pt for choosing the attribute, 1 pt for comparison to X
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