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STAB22 Past Final solutions 07
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University of Toronto ScarboroughSTAB22 Final Examination
December 2010
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. A study was carried out to determine whether a new diet is effective in reducing
cholesterol levels. Twenty subjects were recruited. For each subject, the cholesterol
level was measured initially. Each subject was placed on the new diet for one month,
and then that subject’s cholesterol level was measured again. Which of the following
methods of analysis is most appropriate?
(a) * One-sided matched pairs t test.
(b) Two-sided two-sample z-test
(c) Two-sided two-sample t test.
(d) One-sided two-sample t test.
(e) Two-sided matched pair t test.
2. A medical treatment has a success probability of 0.7. Three patients will be treated
with this treatment. Assuming the results are independent for the three patients, what
is the probability that at least one of them will be successfully cured?
1-0.3^3=0.973 or use Table C n=3, p=0.7
(a) 0.70
(b) 0.50
(c) * 0.97
(d) 0.99
(e) 0.21
3. The distribution of the weight of chocolate bars produced by a certain machine has
mean of 8.1 oz and a standard deviation of 0.1 oz. The quality control manager plans
to take a simple random sample from the production line. How big should the sample
size n be so that the sampling distribution of the sample mean has standard deviation
0.02 oz?
sigma/sqrt(n)=0.02=0.1/sqrt(n), so sqrt(n)=5 and n=25.
(a) * 25
(b) 100
(c) 5
(d) Cannot be determined unless we know the population follows a Normal distribu-
tion.
(e) 10
2
,4. A study was conducted to examine the quality of fish after seven days in ice storage.
In the output below, y denotes a measurement of fish quality (on a 10-point scale)
and x denotes the time (in hours) after being caught that the fish were placed in ice
packing. The scatterplot of y versus x showed a linear relationship. Some output is
shown below.
Regression Analysis: y versus x
The regression equation is
y = 8.43 - 0.144 x
Predictor Coef SE Coef T P
Constant 8.4318 0.1018 82.86 0.000
x -0.14402 0.01391 -10.36 0.000
S = 0.187052 R-Sq = 92.3% R-Sq(adj) = 91.4%
Analysis of Variance
Source DF SS MS F P
Regression 1 3.7524 3.7524 107.25 0.000
Residual Error 9 0.3149 0.0350
Total 10 4.0673
What is the value of the correlation between x and y?
sqrt(0.923) = 0.96072889 and the correlation is negative since the
slope is negative.
(a) -0.923
(b) 0.923
(c) 0.961
(d) * -0.961
(e) 9.61
3
, 5. One of the fish specimens in Question 4 above was placed in ice packing 3 hours after
being caught and had a fish quality rating of 6. What is the residual for this fish
specimen?
predicted quality is 8.43-(0.144)(3)=7.998 (or 8 using more accurate
figures). Residual is 6-8=-2.
(a) * -2
(b) 8
(c) 2
(d) 6
(e) -8
6. In the analysis in Question 4 above, a plot was also made of residuals against x. What
would you expect this residual plot to look like?
(a) Has a downward non-linear trend.
(b) Has a “fanning-out” pattern.
(c) Has a linear trend.
(d) Has a curved pattern.
(e) * Has no pattern.
7. Two alloys, A and B, are used in the manufacture of steel bars. A study was carried
out to compare the load capacities of bars made from the two alloys. (Load capacity
is measured in tons.) The researchers collected data from simple random samples of 9
bars made from alloy A and 13 bars made from alloy B. Let µA denote the population
mean load capacity of bars made from alloy A, and let µB denote the population mean
load capacity of bars made from alloy B. You may assume that load capacities in the
samples have normal distributions. Some output from an analysis is shown below.
Sample 1 is alloy A, and sample 2 is alloy B.
4
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