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STAB22 Past Final solutions 04
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University of Toronto ScarboroughSTAB22 Final Examination
April 2008
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 16 numbered pages; before you start,
check to see that you have all the pages. There are statistical
tables at the back.
This examination is multiple choice. Each question has equal
weight, and there is no penalty for guessing. 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.)
If you need paper for rough work, use the back of the sheets of this
question paper. The question paper will be collected at the end of
the examination, but any writing on it will not be read or marked.
Before you begin, two 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 in-
vigilator collects it. The signature sheet shows that you were
present at the exam.
1
,1. Systolic blood pressure readings of individuals are thought to be related to weight. The following
MINITAB output was obtained from a regression analysis of systolic blood pressure on weight (in
pounds). Use this information to answer this question and the next question. Answer these questions
assuming that the regression model given in the in the MINITAB output is appropriate.
Descriptive Statistics: Systolic, Weight
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Systolic 14 0 154.50 1.49 5.57 145.00 150.75 153.50 158.50
Weight 14 0 194.07 7.18 26.86 164.00 173.00 188.00 212.00
Correlations: Systolic, Weight
Pearson correlation of Systolic and Weight = 0.635
The regression equation is
Systolic = 129 + 0.132 Weight
Predictor Coef StDev T P
Constant 128.935 9.055 14.24 0.000
Weight 0.13173 0.04625 2.85 0.015
2
, Which of the following statements based on the above information is true?
(a) none of the other statements is true
(b) * an increase of 10 pounds in weight is accompanied by an average increase of 1.32 in systolic
blood pressure where systolic blood pressure is measured in the same units as in data.
(c) the normal probability plot of residuals shows that the residuals have a clearly non-normal distri-
bution.
(d) more than one of the other statements is true.
(e) more than 60% of the variation in systolic blood pressure has been accounted for by the linear
relationship with weight.
2. Using the information in Question 1 above, which of the following statements is true?
(a) * none of the other statements is true
(b) more than one of the other statements is true.
(c) If we omit the heaviest person from the data set, the correlation between weight and systolic
blood pressure will be less than 0.635.
(d) In the data above, the weight is measured in pounds. If we convert these weights to kilograms (1
pound = 0.454 kg), then the estimated slope of the regression of systolic blood pressure on weight
will become 0.132 × 0.454.
(e) If we omit the heaviest person from the data set, the slope of the least-squares line (regressing
systolic on weight) will be less than 0.132.
3. A statistics class had 60 female students and 40 male students. MINITAB descriptive statistics of the
scores on the final exam for this class are given below:
Descriptive Statistics: Score
Sex N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
Female 60 63.70 2.02 15.68 30.00 50.00 60.00 77.50 92.00
Male 40 57.35 1.98 12.52 24.00 50.00 60.00 60.00 80.00
The class average, (i.e. the mean of all 100 students) to the nearest single decimal place is:
(a) This cannot be calculated from the information given
(b) 63.0
(c) 60.0
(d) * 61.2
(e) 60.5
4. A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity
of a randomly selected tank has a normal distribution with a mean of 15.0 gallons and a standard
deviation of 0.15 gallons. Use this information for this question and the following one.
The manufacturer of this gasoline tank considers the largest 2% of these tanks as too large to put on
the market. What is the minimum capacity (in gallons, rounded to two decimal places) that will be
considered as too large?
(a) 16.00 gallons
(b) 15.72 gallons
(c) * 15.31 gallons
(d) 15.00 gallons
3
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