Math 1070–1
Midterm Exam #1
Name:
Student Number:
You have 50 minutes to take this examination. This is to be a closed book
test. You may, however, use a hand calculator. Do not attach other sheets
of paper to this test booklet. You may use both sides of the paper provided
to you. Incomplete answers or solutions with insufficient explanation of the
methods do not merit any partial credit. Incorrect explanations result in
loss of earned points; so limit your explanations to answers that you well
understand. There are 5 questions in 5 pages including a scratch sheet of
paper; be sure to read/use them all.
—Grade Distribution—
Question
Number
1
2
3
4
5
Total
Points
Possible
5
6
6
5
8
30
Points
Earned
1. (5 points) The average Verbal SAT score in 1994 was about 466, and
the standard deviation was 110. If these scores are normally distributed
(which they were), the percentage of students who scored over 600 in
1994 was (circle the closest answer):
(i) 91%; (ii) 9%; (iii) 89%; (iv) 11%; (v) other
1
2. (3 points each) Consider the following data set: 35, 24, 46, 77, 111, 103, 255, 903, 777.
(a) Find the five number summary for this data.
Put your final five numbers in these boxes in the correct order:
,
,
,
,
.
(b) Use the “1.5 × IQR Criterion” to find all (or any) of the outliers.
2
3. Consider the following data; it is part of the 1989 Per Capita income
data for the United States:
Alabama
Alaska
Arizona
Arkansas
California
Colorado
13,679
21,173
15,881
12,984
19,740
17,494
(a) (2 points) Which is a possible/valid way to represent this data
(Circle one, none, or both):
(i) A histogram; (ii) a bar graph.
(b) (4 points) Plot the graph that you circled in part (a).
3
4. (5 points) There is a substantial amount of modern medical research
(UCA–Davis) that shows that “drinking a moderate amount of wine
per day reduces the risk of coronary heart disease.” Nearly all of these
studies achieve this by demonstrating, in one way or another, that there
is a strong negative association between wine consumption (glasses per
day at the moderate level of 1–3 glasses per day) and the risk of coronary heart disease. Argue why such arguments can be seriously flawed.
[Deductions will be for writing answers that are incorrect or not immediately relevant. So it is possible to end up with a negative score on
this problem! Keep it short, as well as well though-out.]
4
5. The gas mileage of an automobile first increases and then decreases
as the speed increases. Suppose that this relationship is very regular,
as shown by the following data on speed (miles per hour) and mileage
(miles per gallon):
Speed
20
30
40
50
60
MPG
24
28
30
28
24
(a) (4 points) Make a scatterplot of mileage versus speed, after correctly identifying the response and explanatory variables.
(b) (4 points) Compute the correlation by showing all of the details
of the calculation; a numerical answer will not earn any partial
credit. [Show your work on this and the next page.]
5
Workspace for Question 5
6
Some Formulas
1. Standard Deviation.
r
sx =
2. Correlation.
1 X
(x − x̄)2 .
n−1
1 X
r=
n−1
x − x̄
sx
y − ȳ
sy
3. The regression line.
rsy
rsy
ŷ =
x + ȳ −
x̄ .
sx
sx
7
.