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STAB22 Past Final solutions 08
STAB22 Past Final solutions 08
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University of Toronto ScarboroughSTAB22 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 31 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. When computing a confidence interval for the population mean µ when the population
SD σ is known, what value of z ∗ should be used √ for an 85% confidence interval? (The
∗
formula for the confidence interval is x̄ ± z σ/ n.)
(612.tex) 85% in the middle leaves 15% for the ends, or 0.075 for each
end. Looking up 0.0750 in the body of table A gives z=-1.44, so
7.5\% is below -1.44 and 7.5% is above z=1.44. Hence z*=1.44.
(a) 1.84
(b) 1.96
(c) 1.64
(d) 1.26
(e) * 1.44
2. Let x̄ be the mean of a random sample of size 4 from a Normally distributed popula-
tion with mean 10 and standard deviation 20. What can we say about the sampling
distribution of x̄ ?
(513.tex) A) will not have a Normal distribution because of the small sample siz
B) The distribution of will be approximately Normal but not very close to a Norm
C) will have a Normal distribution with mean 10 and standard deviation 20.
D) will have a Normal distribution with mean 20 and standard deviation 20.
E) will have a Normal distribution with mean 10and standard deviation 10.
Ans E)
When the population is Normal the sample size doent have to be large
for the sample mean to have a Normal distribution. Stad dev =
20/sqrt(4) = 10
(a) * Normal with mean 10 and standard deviation 10.
(b) Only approximately Normal because of the small sample size.
(c) Not Normal because of the small sample size.
(d) Normal with mean 20 and standard deviation 20.
(e) Normal with mean 10 and standard deviation 20.
2
,3. A study was carried out on some people who had developed a cold within the previous
24 hours. The people were randomly divided into two groups; the people in the first
group had to take zinc lozenges, and the people in the second group had to take placebo
lozenges. Everyone was instructed to take the lozenges every 2–3 hours until the cold
was gone. The lozenges were designed so that they could not be distinguished by
anyone involved in giving the lozenges to the subjects. For each person, the overall
duration of cold symptoms was measured.
What kind of study is this?
(311.tex) the subjects are made to take a particular kind of lozenges, so
it’s an experiment. The design of the lozenges makes it
double-blind.
(a) a voluntary-response sample
(b) * a double-blind experiment
(c) an observational study
(d) a stratified sample
(e) an experiment, but not double-blind
3
, 4. The marks in an exam have a Normal distribution with mean 65 and standard deviation
15. A mark of 80 or above qualifies for an A grade. Adam, Bob and Cindy are three
students writing this exam. Assume that their marks are independent. What is the
probability that that at least one of them will get an A grade?
(524.tex) A) 0.16
B) 0.05
C) 0.4
D) 0.06
E) 0.5
Ans C)
P(A) = 0.8413 and probability none of them will get an A = 0.8413^3 = 0.59546010
Or with 68-95-99.5 % rule,, 1- 0.84^3 = 0.407296
(a) 0.16
(b) * 0.4
(c) 0.5
(d) 0.05
(e) 0.06
4
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