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UNIVERSITY OF TORONTO SCARBOROUGHDepartment of Computer and Mathematical Sciences
Midterm Test October 2013
STAB22H3 Statistics I
Duration: 1 hour and 45 minutes
Last Name: First Name:
Student number:
Aids allowed:
- One handwritten letter-sized sheet (both sides) of notes prepared by you
- Non-programmable, non-communicating calculator
Standard normal distribution tables are attached at the end.
This test is based on multiple-choice questions. There are 30 questions. All questions carry
equal weight. On the Scantron answer sheet, ensure that you enter your last name, first
name (as much of it as fits), and student number (in “Identification”).
Mark in each case the best answer out of the alternatives given (which means the nu-
merically closest answer if the answer is a number and the answer you obtained
is not given.)
Also before you begin, complete the signature sheet, but sign it only when the invigilator
collects it. The signature sheet shows that you were present at the exam.
Good luck!!
ExamVersion: A
1
,1.
The table below gives the results of a survey of 800 college seniors regarding their
undergraduate major and whether or not they plan to go to graduate school.
Graduate School Business Engineering Others
Yes 70 84 126
No 182 208 130
What percentage of the students does not plan to go to graduate school?
(a) 280
(b) 65
(c) 32
(d) 35
(e) 25
2. Using the data in question 1 above, among those students who are majoring in business,
what percentage plans to go to graduate school?
(a) 27.78
(b) 8.75
(c) 72.22
(d) 70
(e) 31.5
3. Using the data in question 1 above, among the students who plan to go to graduate
school, what percentage is business majors?
(a) 27.78
(b) 8.75
(c) 72.22
(d) 70
(e) 25
2
,4. For simple linear regression, the fitted regression line obtained using the method of
least squares is
(a) the line which makes the sample correlation coefficient as close to +1 or -1 as
possible.
(b) the line which best splits the data in half, with 50% of the data points lying
above the regression line and 50% of the data points lying below the fitted
regression line.
(c) the line which minimizes the number of data points that do not pass through
the regression line.
(d) the line that minimizes the sum of the squared residuals.
(e) the line which guarantees that the error terms will be normally distributed.
5. The boxplots below displays a comparison of blood cholesterol measurements for three
groups of people (group A, B and C):
Read the following statements based on the above boxplots:
I The third quartile for group A is less than the first quartile for group B.
II More than 25 percent of the people in group C have higher cholesterol levels than
the person with the highest level in group A.
III The median for group B is greater than the mean for group B.
The above statements may or may not be true. Based on the information in the
boxplots above, which statement is true?
(a) Only statement I is true
(b) Only statement II is true
(c) Only statements I and II are true
(d) Only statements II and III are true
(e) none is true
3
, 6. New recruits to the Canadian military have head circumferences that are Normally
distributed with mean of 65 cm, and standard deviation of 4 cm. One percent of the
helmets manufactured for the recruits should have circumferences bigger than what
size?
(a) 63.06 cm
(b) 80.9 cm
(c) 74.3 cm
(d) 91.23 cm
(e) 68.9 cm
7. For a simple linear regression model, suppose we fitted a least squares regression line
and obtained ŷ = 5 + 3x . What is the residual associated with the point (x, y) =
(4, 19)?
(a) -13
(b) -2
(c) 13
(d) 17
(e) 2
4
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