Exam

Premium

Department

Statistics

Course Code

STAB22H3

Professor

All

Study Guide

Final

University of Toronto Scarborough

STAB22 Final Examination

December 2009

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 in-

vigilator 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. Heart problems can be examined via a small tube (called a catheter) threaded into the heart from a

vein in the patient’s leg. It is important that the company that manufactures the catheter maintains

a diameter of 2 mm. Suppose µdenotes the population mean diameter. Each day, quality control

personnel make measurements to test a null hypothesis that µ= 2.00 against an alternative that

µ6= 2.00, using α= 0.05. If a problem is discovered, the manufacturing process is stopped until the

problem is corrected.

What, in this context, is a type II error?

(a) Concluding that the mean catheter diameter is not 2 mm when it is actually less than 2 mm.

(b) * Concluding that the mean catheter diameter is satisfactory when in fact it is either bigger or

smaller than 2 mm.

(c) Using a sample size that is too small.

(d) Concluding that the mean catheter diameter is 2 mm when it actually is 2 mm.

(e) Concluding that the mean catheter diameter is unsatisfactory when in fact it is equal to 2 mm.

A Type II error is failing to reject the null when it is in fact wrong. In this case, the mean

is actually not 2, but we cannot reject the null hypothesis that it is 2. This is (b).

2. The Kentucky Derby is a famous horse race that has been run every year since the late 19th century.

The scatterplot below shows the speed (in miles per hour) of the winning horse, plotted against the

year. The regression line is shown on the plot.

What kind of association do you see between speed and year?

(a) no association

(b) negative and non-linear

(c) negative and linear

(d) positive and linear

(e) * positive and non-linear

The pattern is not absolutely clear, but it does seem that on average the speed is higher

when the year number is higher (that is, more recently). So the association is positive. Is

it linear? Well, the majority of observations are below the line at the left and right ends,

and above the line in the middle, so it looks as if a non-linear association would be a better

description of what’s going on. This is reasonable because you’d guess that there is a lot

of “room for improvement” in the early years, but now, any breaking of the speed record is

going to be only by a small amount.

3. Weighing large trucks is a slow business because the truck has to stop exactly on a scale. This is

called the “static weight”. The Minnesota Department of Transportation developed a new method,

called “weight-in-motion”, to weigh a truck as it drove over the scale without stopping. To test the

2

eﬀectiveness of the “weight-in-motion” method, 10 trucks were each weighed using both methods. All

weights are measured in thousands of pounds.

A scatterplot of the results is shown below. Superimposed on the scatterplot is the line that the data

would follow if the weight-in-motion was always equal to the static weight. Use the scatterplot to

answer this question and the one following.

How would you describe the positive association?

(a) not useful since the data are not close to the line

(b) * approximately linear

(c) deﬁnitely curved

(d) no association of note

The line on the plot is a bit of a distraction, because the points form a more or less linear

pattern, just not around the line shown. (The trend in the points is not obviously a curve,

at least).

4. Question 3 described some data on two methods of weighing trucks. The Minnesota Department of

Transportation wants to predict the static weight of trucks from the weight-in-motion. Which of the

following statements best describes what they can do?

(a) * taking the weights-in-motion and modifying them in some linear way would accurately predict

the static weight.

(b) The weights-in-motion can be used to predict the static weights, but a non-linear transformation

would have to be applied to do it.

(c) The static weight is accurately predicted by the weight-in-motion itself.

(d) There is no way to use the weights-in-motion to predict the static weight.

Since there is a linear association (just not of the form y=x), the static weight can be

predicted reasonably well from the weight-in-motion, by multiplying the weight-in-motion

by something and adding something else — that is, by using the linear regression equation.

5. A factory hiring people to work on an assembly line gives job applicants a test of manual agility.

This test involves ﬁtting strangely-shaped pegs into matching holes on a board. In the test, each job

applicant has 60 seconds to ﬁt as many pegs into their holes as possible. For one job application cycle,

the results were as follows:

Male applicants Female applicants

Subjects 41 51

Mean pegs placed 17.9 19.4

SD of pegs placed 2.5 3.4

The factory wishes to see if there is evidence for a diﬀerence between males and females. Which is

more appropriate, a matched-pairs t-test or a two-sample t-test? Using the more appropriate test,

what P-value do you obtain?

3

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