University of Toronto Scarborough
STAB22 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 25 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 community is considering building a new skateboard park, and wants to survey
people’s opinions. Younger people might have a different opinion about the skateboard
park than older people, so, to ensure that each age group is properly represented,
separate simple random samples are taken from the different age groups, and the
results are combined. What is this sampling method called?
(a) systematic sampling
(b) quota sampling
(c) stratified sampling
(d) simple random sampling
(e) multistage sampling
2. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures
the motivation, attitude, and study habits of college students. Scores follow a Normal
distribution with mean 115 and standard deviation 25. You suspect that incoming
freshmen at your school have a mean that is different from 115, because they may
be excited yet anxious about entering college. Let µ be the mean SSHA score of all
incoming freshmen at your school. You decide to test the hypotheses H0 : µ = 115
versus Ha : µ 6= 115. The value of the Z-test statistic based on a random sample of 25
incoming freshmen was found to be z = 0.24 (assuming σ = 25). Calculate the upper
limit of the 95% confidence interval for µ, again assuming σ = 25.
(a) 131
(b) 124
(c) 126
(d) 125
(e) 136
2
, 3. 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?
(a) -0.961
(b) 0.923
(c) 0.961
(d) 9.61
(e) -0.923
4. One of the fish specimens in Question 3 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?
(a) -8
(b) 2
(c) -2
(d) 8
(e) 6
3
STAB22 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 25 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 community is considering building a new skateboard park, and wants to survey
people’s opinions. Younger people might have a different opinion about the skateboard
park than older people, so, to ensure that each age group is properly represented,
separate simple random samples are taken from the different age groups, and the
results are combined. What is this sampling method called?
(a) systematic sampling
(b) quota sampling
(c) stratified sampling
(d) simple random sampling
(e) multistage sampling
2. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures
the motivation, attitude, and study habits of college students. Scores follow a Normal
distribution with mean 115 and standard deviation 25. You suspect that incoming
freshmen at your school have a mean that is different from 115, because they may
be excited yet anxious about entering college. Let µ be the mean SSHA score of all
incoming freshmen at your school. You decide to test the hypotheses H0 : µ = 115
versus Ha : µ 6= 115. The value of the Z-test statistic based on a random sample of 25
incoming freshmen was found to be z = 0.24 (assuming σ = 25). Calculate the upper
limit of the 95% confidence interval for µ, again assuming σ = 25.
(a) 131
(b) 124
(c) 126
(d) 125
(e) 136
2
, 3. 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?
(a) -0.961
(b) 0.923
(c) 0.961
(d) 9.61
(e) -0.923
4. One of the fish specimens in Question 3 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?
(a) -8
(b) 2
(c) -2
(d) 8
(e) 6
3
