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STAB22 Past Midterm solutions 05
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University of Toronto ScarboroughSTAB22 Midterm Examination
October 2009
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 16 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 wrote, all your questions are in here somewhere.
1. Look at the experiment depicted below.
Treatment 1
Mike, Joe, Mary, Jill ----- record results
/
Subjects: /
Mike, Joe, Mary, Jill \
\
Treatment 2
Mike, Joe, Mary, Jill ----- record results
Who is Mike matched with?
(a) Mary
(b) treatment one
(c) * himself
(d) treatment two
(e) both treatments one and two
All four people do both treatments, so they are matched in some way. Under treatments
1 and 2, they are listed in the same order, so they are matched with themselves (it is the
kind of experiment where you get two measurements from each person, like a “before” and
“after”). So Mike is matched with Mike.
2. The scatterplot below shows the association between a variable x and a variable y, with the regression
line superimposed. Use the scatterplot to answer this question and the one following.
How would you describe the point with x = 400?
(a) Having a large negative residual
(b) * Influential
(c) Outlier
The point over on the right is, in x terms, a long way from the other points, so it is likely
to be influential on the regression line. This is confirmed if you look at the picture more
carefully: a line going through the cloud of points on the left would be less steep than the
line shown, so the line’s slope is being dragged upwards by the isolated observation on the
right.
2
, 3. In the scatterplot of Question 2, what would happen if the point with x = 400 were removed?
(a) * The slope must become less
(b) The slope would not change
(c) The correlation must become lower
(d) The slope must become greater
Ask yourself what would be the best line without the point on the right: one with a smaller
slope. That offers (a) as an option. The correlation might go up or down; sometimes removing
an influential point makes it bigger, sometimes smaller. So (c) isn’t necessarily true.
4. When I ride the bus to school, I note how many minutes the journey takes. My last 10 journeys had
a mean length of 37 minutes. Which of the following names describes the 37 minutes?
(a) parameter
(b) * statistic
(c) census
(d) sampling variability
(e) sample
My last 10 journeys are only a sample of “all possible journeys”, so this is a statistic. If
I were talking about all journeys, then it would be a parameter. A sample is the process
producing the mean, not the value that is (or might be) produced.
5. Dairy inspectors visit Ontario farms unannounced and take samples of the milk. If the milk is found
to contain dirt, antibiotics or other foreign matter, the day’s milk output from the farm is destroyed
(and the farm re-inspected until the purity of the milk is satisfactory).
Suppose the dairy inspectorate’s farm sampling procedure is as follows: First, randomly select a sample
of Ontario counties. Then, within each selected county, take a simple random sample of dairy farms.
Then, visit each of the sampled dairy farms.
What kind of sampling procedure is this?
(a) * Multistage sample
(b) Stratified sample
(c) Systematic sample
(d) Simple random sample
(e) Voluntary-response sample
What makes it multistage is the selection of counties first, and then farms from within the
selected counties. (Compare making a list of all dairy farms in Ontario, and then selecting
from that: this would be a simple random sample.)
6. Look at the experiment depicted below.
Treatment One: Mike ------------ record data
/ Treatment Two: Joe ------------ record data
/
Subjects /
Mike, Joe, Mary, Jill \
\
\ Treatment One: Mary ------------ record data
Treatment Two: Jill ------------ record data
3
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