University of Toronto Scarborough
STAB22 Final Examination
December 2011
For this examination, you are allowed two handwritten letter-sized sheets of notes
(both sides) prepared by you, a non-programmable, non-communicating calculator,
and writing implements.
This question paper has 22 numbered pages, with statistical tables at the back.
Before you start, check to see that you have all the pages. You should also have a
Scantron sheet on which to enter your answers. If any of this is missing, speak to
an invigilator.
This examination is multiple choice. Each question has equal weight, and there is
no penalty for guessing. To ensure that you receive credit for your work on the
exam, fill in the bubbles on the Scantron sheet for your correct student number
(under “Identification”), your last name, and as much of your first name as fits.
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.)
If you need paper for rough work, use the back of the sheets of this question paper.
Before you begin, two more things:
• 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.
• Complete the signature sheet, but sign it only when the invigilator collects it.
The signature sheet shows that you were present at the exam.
At the end of the exam, you must hand in your Scantron sheet (or you will receive a
mark of zero for the examination). You will be graded only on what appears on the
Scantron sheet. You may take away the question paper after the exam, but whether
you do or not, anything written on the question paper will not be considered in your
grade.
1
,1. For each of a number of cities across Canada, the number of people with Cantonese as
a mother tongue and the number of people with Mandarin as a mother tongue were
recorded. A scatterplot of the data is shown below.
The correlation between the number of Cantonese speakers in a city and the number
of Mandarin speakers is 0.980. Do you think this correlation is a reasonable summary
of the relationship? Why, or why not?
(a) If the two largest cities (Toronto and Vancouver) were removed, the correlation
would be even higher.
(b) No, because there are outliers and/or influential points.
(c) Yes, because the relationship is more or less linear.
(d) No, because the relationship is clearly curved.
(e) Yes, because there are no influential points.
2
, 2. In a game you toss a fair coin once. You win $20 if a head comes up and you lose $10
if a tail comes up. Let the random variable X denote the amount of money you win.
(Losing $10 means winning −$10.) What is the standard deviation of X, in dollars?
(a) 15
(b) 12.50
(c) 17.50
(d) 10
(e) 5
3. A 98% confidence interval was calculated for a population mean, based on a simple
random sample of size 25. The population standard deviation was not known. The
interval was from 54 to 66. What must the standard deviation of this sample have
been?
(a) 6
(b) 12
(c) 10
(d) 14
(e) 5
3
STAB22 Final Examination
December 2011
For this examination, you are allowed two handwritten letter-sized sheets of notes
(both sides) prepared by you, a non-programmable, non-communicating calculator,
and writing implements.
This question paper has 22 numbered pages, with statistical tables at the back.
Before you start, check to see that you have all the pages. You should also have a
Scantron sheet on which to enter your answers. If any of this is missing, speak to
an invigilator.
This examination is multiple choice. Each question has equal weight, and there is
no penalty for guessing. To ensure that you receive credit for your work on the
exam, fill in the bubbles on the Scantron sheet for your correct student number
(under “Identification”), your last name, and as much of your first name as fits.
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.)
If you need paper for rough work, use the back of the sheets of this question paper.
Before you begin, two more things:
• 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.
• Complete the signature sheet, but sign it only when the invigilator collects it.
The signature sheet shows that you were present at the exam.
At the end of the exam, you must hand in your Scantron sheet (or you will receive a
mark of zero for the examination). You will be graded only on what appears on the
Scantron sheet. You may take away the question paper after the exam, but whether
you do or not, anything written on the question paper will not be considered in your
grade.
1
,1. For each of a number of cities across Canada, the number of people with Cantonese as
a mother tongue and the number of people with Mandarin as a mother tongue were
recorded. A scatterplot of the data is shown below.
The correlation between the number of Cantonese speakers in a city and the number
of Mandarin speakers is 0.980. Do you think this correlation is a reasonable summary
of the relationship? Why, or why not?
(a) If the two largest cities (Toronto and Vancouver) were removed, the correlation
would be even higher.
(b) No, because there are outliers and/or influential points.
(c) Yes, because the relationship is more or less linear.
(d) No, because the relationship is clearly curved.
(e) Yes, because there are no influential points.
2
, 2. In a game you toss a fair coin once. You win $20 if a head comes up and you lose $10
if a tail comes up. Let the random variable X denote the amount of money you win.
(Losing $10 means winning −$10.) What is the standard deviation of X, in dollars?
(a) 15
(b) 12.50
(c) 17.50
(d) 10
(e) 5
3. A 98% confidence interval was calculated for a population mean, based on a simple
random sample of size 25. The population standard deviation was not known. The
interval was from 54 to 66. What must the standard deviation of this sample have
been?
(a) 6
(b) 12
(c) 10
(d) 14
(e) 5
3
