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University of Toronto ScarboroughSTAB22 Final Examination
December 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 18 numbered pages. Before you start,
check to see that you have all the pages. In addition, 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 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.
1
,Version: pink
1. An industrial process produces items of which 80% conform to specifications. An inspector will take
a random sample of 100 items. In the sample, the probability that x or more items will conform to
specifications is 0.30. What, using a suitable approximation, is x?
(a) 78
(b) 90
(c) 82
(d) 70
(e) 55
2. A local country club operates facilities that include a golf course and tennis courts. A survey of the
members indicates that 72% regularly use the golf course, 42% regularly use the tennis courts and 8%
use neither of these facilities regularly. (Some members play both golf and tennis.) Use this information
for this question and the next one.
The club has 600 members. How many members regularly use at least one of the golf or tennis facilities?
(a) 552
(b) 276
(c) 424
(d) 578
(e) 244
3. Suppose that we randomly selected one of the members of the country club mentioned in Question 2.
The probability that this member regularly uses exactly one facility is
(a) 0.79
(b) 0.50
(c) 0.17
(d) 0.29
(e) 0.70
4. A population mean is known to be 20. A simple random sample of 80 individuals is drawn from this
population. What can you say about what the sample mean might be?
(a) it will be exactly 20
(b) it could be anything
(c) it could be anything, but will probably be close to 20
5. A fraud investigator is investigating a group of physicians accused of forging their bills. The physicians
work at three different hospitals (labelled A, B and C). The investigator’s goal is to estimate the
overall proportion of forged bills. It is known that bills from hospital A are very hard to forge. The
investigator only has resources to sample 10% of the relevant bills. What sampling method might the
investigator use?
(a) Multi-stage sample
(b) Stratified sample
(c) Simple random sample
(d) Block design
(e) Systematic sample
2
, 6. Travel times for buses on a certain journey have a mean of 22 minutes and a standard deviation of 3
minutes. The travel times have a normal distribution. Use this information for this question and the
next one.
What is the probability that on a randomly chosen day, the journey will take more than 24 minutes?
(a) 0.75
(b) 0.50
(c) 0.25
(d) 0.35
(e) 0.10
7. Refer to Question 6. The journey described there is made on 10 randomly chosen days. What is the
probability that the sample mean travel time on those days is greater than 24 minutes?
(a) 0.98
(b) 0.30
(c) 0.70
(d) 0.02
(e) Same answer as Question 6
8. A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local brewery.
The company receives a complaint that their bottles are not holding enough liquid. To assess the
evidence for this complaint, the bottling company randomly samples 64 bottles and finds that the
average amount of liquid held by the 64 bottles is 11.915 ounces with a sample standard deviation of
0.40 ounces. Suppose that the P-value of this test turned out to be 0.0446. The proper conclusion
from this test is:
(a) We fail to reject the null hypothesis at α = 0.05
(b) There is evidence that the company bottles are not holding enough liquid at α = 0.05.
(c) There is evidence that the company bottles are not holding enough liquid at α = 0.025.
(d) There is not enough information to make any conclusion.
(e) We reject the null hypothesis at α = 0.01.
9. We want to examine and compare the effects on digestion of taking varying amounts of a certain drug:
0, 25, 50, 75 mg. What kind of experimental design might we use?
(a) Block design
(b) Matched pairs design
(c) Systematic sample
(d) Completely randomized design
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