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STAB22 Past Final with Solutions (Version A and Version B)
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UNIVERSITY OF TORONTO SCARBOROUGHDepartment of Computer and Mathematical Sciences
DECEMBER 2013 EXAMINATIONS
STAB22H3 Statistics I
Duration: 3 hours
Last Name: First Name:
Student number:
Aids allowed:
- Two handwritten letter-sized sheets (both sides) of notes prepared by you
- Non-programmable, non-communicating calculator
Standard Normal, t and the binomial distribution tables are attached at the end.
This test is based on multiple-choice questions. There are 44 questions. All questions carry
equal weight. 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 nu-
merically closest answer if the answer is a number and the answer you obtained
is not given.)
Also before you begin, complete the signature sheet, but sign it only when the invigilator
collects it. The signature sheet shows that you were present at the exam.
Good luck!!
ExamVersion: A
1
,1. In a study of acupuncture for treating pain, 100 volunteers were recruited. Half were
randomly assigned to receive acupuncture and the other half to receive a sham acupunc-
ture treatment. The patients were followed for 6 months and the treating physician
measured their degree of pain relief. The patients did not know which treatment they
actually received, but the treating physicians were aware of who was getting acupunc-
ture and who wasn’t. Which of the following best describes this study?
(a) This is a retrospective observational study.
(b) This is a randomized block design.
(c) This is a randomized single-blind experiment.
(d) This is a randomized double-blind experiment.
(e) This is a prospective observational study.
2. Which of the following pairs of events (denoted by A and B) are disjoint and indepen-
dent?
(a) Toss two coins, A = first toss is head, B = second toss is head
(b) Roll a die, A = observe an odd number, B = observe an even number
(c) Take two cards one by one from a deck of 52 cards, A = first card is red, B =
both cards are red
(d) There are three kids in a family, A = two kids are girls, B = two kids are twins
(e) None of the above
3. In a group of 100 people, 40 own a cat, 25 own a dog, and 15 own a cat and a dog.
Find the probability that a person chosen at random, owns a dog, given that he owns
a cat.
(a) 0.375
(b) 0.6
(c) 0.25
(d) 0.4
(e) 0.15
2
,4. Two stores (store A and store B) sell watermelons. The weights of watermelons at store
A has a Normal distribution with mean 21 pounds and standard deviation 3 pounds.
The weights of watermelons at store B has a Normal distribution with mean 18 pounds
and standard deviation 2 pounds. The weights of watermelons at the two stores are
independent. If you select a melon at random at each store, what is the probability
that melon you selected at store B will be heavier? Choose the closest.
(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4
(e) 0.5
5. The regression equation relating midterm score (x) and final exam score (y) in a course
is y = 20+0.8x. Which of the following is a valid conclusion based on this information?
(a) If Adam has scored 10 points higher than Bob on the midterm, then Adam will
score 8 points higher than Bob on the final exam.
(b) Students who score 80 on the midterm are predicted to score 84 on the final.
(c) If a student scores 0 on the midterm, then that student will score 20 on the
final.
(d) On average, the students’ scores on the final exam will only be 80% of what
they were on the midterm.
(e) This equation shows that the midterm and the final exam scores are not related.
6. A test of significance with α = 0.05 results in a P-value of 0.1. What do you conclude?
(a) Reject the null hypothesis.
(b) Reject the alternative hypothesis.
(c) Do not reject the alternative hypothesis.
(d) Do not reject the null hypothesis.
(e) Accept the null hypothesis.
3
, 7. The pie chart below shows the percentage of students in each faculty at a university.
Pie Chart of Percentage vs Faculty
A rts
25.0%
Science
35.0%
Business
15.0%
Engineering
10.0% Education
Medicine Law 5.0%
5.0% 5.0%
If the number of students in the faculty of Arts is 3000, then how MANY students are
there in the faculty of Science?
(a) 3400
(b) 3600
(c) 3800
(d) 4000
(e) 4200
8.
The two-way table below classifies the members of a fitness club by gender and food
habits. Use this information to answer this question and the next question.
Women Men
Vegetarian 9 3
Non-vegetarian 8 10
If a member is selected at random from the club, what is the probability that this
person is a vegetarian female?
(a) 3/4
(b) 3/10
(c) 1/10
(d) 4/9
(e) 9/17
4
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