University of Toronto Scarborough
STAB22 Midterm Examination
March 2008
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 14 numbered pages; before you start,
check to see that you have all the pages. There is also a signature
sheet at the front and statistical tables at the back.
This examination is multiple choice. Each question has 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 numerically closest answer if the answer is a
number and the answer you obtained is not given.)
Before you begin, check that the colour printed on your Scantron
sheet matches the colour of your question paper. If it does not,
get a new Scantron from an invigilator.
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.
1
, Whichever version of the exam you had, all these questions will have been on it, though most likely with
the alternative answers in a different order.
1. A linear regression was carried out for predicting one variable y from another variable x. The residuals
from the regression were calculated and plotted against x. The plot is shown below.
What do you conclude from this plot?
(a) There is no evidence for a straight-line relationship at all between y and x from this graph.
(b) * A straight-line relationship between y and x is a satisfactory fit.
(c) The relationship between y and x is obviously curved.
(d) In the relationship between y and x, y is predicted more accurately for smaller values of x than
for larger values.
(e) To assess the strength and form of the relationship between y and x, it is enough to look at the
correlation; there is no need to look at the residual plot.
This residual plot is a formless mess of nothing, which is the ideal. So the straight line that was fitted
to produce these residuals does describe the data satisfactorily. (Don’t confuse this with a scatterplot
of y vs. x: if this picture had been that scatterplot, then there would indeed have been no evidence of
a relationship.
2. Use the information below for this question and the following two questions.
Scores on a standardized test for children have mean 50 and standard deviation 10, and they follow a
normal distribution.
What proportion of children will score above 65 on this test? (Mark the closest answer below if your
answer does not appear.)
(a) 0.50
(b) 0.93
(c) 0.20
(d) 0.80
(e) * 0.07
z = (65 − 50)/10 = 1.5; the proportion below is 0.93 (from table A), so proportion above is one minus
that.
2
STAB22 Midterm Examination
March 2008
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 14 numbered pages; before you start,
check to see that you have all the pages. There is also a signature
sheet at the front and statistical tables at the back.
This examination is multiple choice. Each question has 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 numerically closest answer if the answer is a
number and the answer you obtained is not given.)
Before you begin, check that the colour printed on your Scantron
sheet matches the colour of your question paper. If it does not,
get a new Scantron from an invigilator.
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.
1
, Whichever version of the exam you had, all these questions will have been on it, though most likely with
the alternative answers in a different order.
1. A linear regression was carried out for predicting one variable y from another variable x. The residuals
from the regression were calculated and plotted against x. The plot is shown below.
What do you conclude from this plot?
(a) There is no evidence for a straight-line relationship at all between y and x from this graph.
(b) * A straight-line relationship between y and x is a satisfactory fit.
(c) The relationship between y and x is obviously curved.
(d) In the relationship between y and x, y is predicted more accurately for smaller values of x than
for larger values.
(e) To assess the strength and form of the relationship between y and x, it is enough to look at the
correlation; there is no need to look at the residual plot.
This residual plot is a formless mess of nothing, which is the ideal. So the straight line that was fitted
to produce these residuals does describe the data satisfactorily. (Don’t confuse this with a scatterplot
of y vs. x: if this picture had been that scatterplot, then there would indeed have been no evidence of
a relationship.
2. Use the information below for this question and the following two questions.
Scores on a standardized test for children have mean 50 and standard deviation 10, and they follow a
normal distribution.
What proportion of children will score above 65 on this test? (Mark the closest answer below if your
answer does not appear.)
(a) 0.50
(b) 0.93
(c) 0.20
(d) 0.80
(e) * 0.07
z = (65 − 50)/10 = 1.5; the proportion below is 0.93 (from table A), so proportion above is one minus
that.
2
