Final Exam Review - Questions
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School
Georgia Institute Of Technology *
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Course
2250
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
13
Uploaded by PresidentWaterWaterBuffalo42
Q1)
The following data give the engine displacement in liters of 30 vehicles sold in a certain country.
С
omplete parts (a) through (f) below.
3.4
3.5
5.5
3.6
3.6
6.1
2.9
2.4
5.9
2.3
3.5
2.1
5.3
2.5
5.6
1.5
2.6
5.5
5.4
6.5
3.4
4.1
3.3
3.4
2.8
5.2
5.3
4.4
3.3
2.5
(a)
Produce a histogram of the engine displacements, with the interval widths set to 0.5 liters and the first
bin starting at 1.25 liter. Describe and interpret the histogram.
Choose the correct graph below.
A.
B.
C.
D.
Describe the histogram. Choose the correct answer below.
A. The distribution of the histogram is multimodal, with modes at 2.5, 4.5, and 5.5 liters.
B. The distribution of the histogram is multimodal, with modes at 2.5, 3.5, and 5.5 liters.
C. The distribution of the histogram is approximately uniform.
D. The distribution of the histogram is unimodal, with most values being large.
Interpret the histogram. Choose the correct answer below.
A. Vehicles with an engine displacement of about 3.5 liters comprise the most common type of vehicle in
this sample.
В
. The different vehicles all have about the same engine displacement.
C. Most of the different vehicles have about the same engine displacement with a few much higher and a
few much lower.
D. A few different vehicles have much higher engine displacement.
(b)
Repeat (a), but with the width of the intervals set to 1 liter and the smallest interval beginning at 1 liter.
Choose the correct graph below.
A.
B.
C.
D.
Describe the histogram. Choose the correct answer below.
A. The distribution of the histogram is approximately uniform.
B. The distribution of the histogram is roughly bimodal, with modes at 2.5 and 4.5 liters.
C. The distribution of the histogram is unimodal, with most values being large.
D. The distribution of the histogram is roughly bimodal, with modes at 3.5 and 5.5 liters.
Interpret the histogram. Choose the correct answer below.
A. Most of the different vehicles have about the same engine displacement with a few much higher and a
few much lower.
B. A few different vehicles have much higher engine displacement.
C. Vehicles with an engine displacement of about 3.5 liters comprise the most common type of vehicle in
this sample.
D. The different vehicles all have about the same engine displacement.
(c) Does the size of the interval width change your impression of the distribution? Explain briefly.
A. Yes; the thinner bins do not accurately show the shape of the distribution.
B. Yes; the wider bins conceal the popularity of engines near 2.5 liters.
C. No; the different bin widths do not change the interpretation of the distribution.
D. No; since the distribution is uniform, the widths of the bins are not affected.
(d)
Find the mean and standard deviation of the engine displacements. How are these related to the
histogram?
The mean
𝑦
̅
is __________ liters. (Round to two decimal places as needed.)
The standard deviation s is __________ liters. (Round to two decimal places as needed.)
How are the mean and standard deviation related to the histogram?
The mean is (1) __________ the histogram.
The standard deviation is (2) __________ the histogram.
Choices for (1):
the balance point of
OR
the middle bar of
OR
the tallest bar of
OR
a measure of the spread
of OR
the shortest bar of
OR
not related to
Choices for (2):
the middle bar of
OR
the tallest bar of
OR
not related to
OR
the shortest bar of
OR
a measure of the spread of
OR
the balance point of
(e)
Find the coefficient of variation and briefly interpret its value.
The coefficient of variation c
v
is __________ . (Round to two decimal places as needed.)
Since the coefficient of variation indicates that the standard deviation is about _________
%
of the mean,
the variation is relatively (3) __________ for this sample. (Round to the nearest integer as needed.)
Choices for (2):
Large
OR
Small
(f)
Identify any unusual values (outliers). What would it mean to be an outlier?
A. The outlier(s) is/are _________ . This/These outlier(s) is/are either a very large or very small engine.
(Use a comma to separate answers as needed.)
B. There are no outliers. An outlier, in this situation, would be a very large or very small engine.
Q2)
The table to the right gives the number of mistakes made by 8 data entry clerks who enter
medical data from case report forms. These forms are submitted by doctors who participate in studies of
the performance of drugs for treating various illnesses. The column Entered indicates the number of
values entered, and the column Errors gives the number of coding errors that were detected among these.
Complete parts a through e.
Entered
Errors
2,829
42
3,770
40
7,749
36
3,803
56
4,239
18
1,529
20
1,740
23
6,280
15
(a)
Make a scatterplot for these data. Which did you choose for the response and which for the
explanatory variable? Describe any patterns. Choose the correct graph below.
A.
B.
C.
D.
Which did you choose for the response and which for the explanatory variable?
O The explanatory variable is Errors and the response is Entered.
O The explanatory variable is Entered and the response is Errors.
Describe any patterns. Choose the correct answer below.
O A. There is a negative then positive curve.
O B. There is a positive linear pattern.
O C. There is little or no pattern.
O D. There is a negative linear pattern.
(b)
Find the correlation r for these data.
r =___________ (Type an integer or decimal rounded to three decimal places as needed.)
(c)
Suppose we were to record the counts in the table in hundreds, so 2,829 became 28.29. How
would the correlation change? Why?
О
A. The correlation would be divided by 10, the square root of 100, because the values are being
divided by 100.
О
B. The correlation would be divided by 100 because the values are being divided by 100.
О
C. The correlation would be multiplied by 100 because the values are being divided by 100.
O D. There would be no change.
(d)
One analyst concluded, "It is clear from this correlation that clerks who enter more values make
more mistakes. Evidently they become tired as they enter more values." Explain why this explanation is
not an appropriate conclusion.
О
A. There's little association between the number entered and the number of errors.
О
B. There's a large association between the number entered and the number of errors.
О
C. The association between the number entered and the number of errors switches from a negative
association to a positive association.
О
D. This is a correct explanation.
Q3)
To gauge the reactions of possible customers, the manufacturer of a new type of cellular telephone
displayed the product at a kiosk in a busy shopping mall. The table to the right summarizes the results for the
customers who stopped to look at the phone. Complete parts (a) through (c) below.
(a)
Is the reaction to the new phone associated with the sex of the customer? How strong is the
association?
Since V = _________ is (1) _________, there is (2) _____________ association between the two
variables. (Round to two decimal places as needed.)
Choices for (1):
rather small
OR
approximately
OR
large
OR
somewhat large
Choices for (2):
moderate
OR
no
OR
strong
OR
weak
(b)
How should the company use the information from this study when marketing its new product?
A. The company should market toward men first since they had a higher percentage of favorable
reactions.
B. Assuming that the reactions of the women sampled are representative of all women, the company
should market toward women first since they had a higher percentage of favorable reactions.
C. Assuming that the reactions of the women sampled are representative of all women, the company
should market toward women first since they had few unfavorable reactions.
D. The company should market toward men first because more men participated in the survey.
(c)
Can you think of an underlying lurking variable that might complicate the relationship shown here?
Justify your answer.
A. Variables such as the proportion that carry a phone, the time of day, or the day of the week are
possible lurking variables because these may be associated with the sex of the customer and also with the
reactions to the new phone.
B. Variables such as the average age of the participants or the median income of the town where the mall
is located are possible lurking variable because people's opinions may be related to the age or wealth.
C. The mall where the data was gathered is the only significant lurking variable because it may have
different types of customers than other malls.
D. There are no lurking variables because the sex of the customer is the only variable that is associated
with the reactions to the new phone.
Male
Female
Favorable
34
20
Ambivalent
48
5
Unfavorable
34
8
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