What is Statistics?
U1-1
Statistics is the set of methods for obtaining,
organizing, summarizing, presenting and analyzing
data.
Our data come from characteristics measured on
individuals or units. These can be people, animals,
places, things, etc.
The po
Examining Relationships
U2-1
In statistics, we often encounter problems which
involve more than one variable. We often want to
compare two (or more) different populations with
respect to the same variable.
We use tools such as side-by-side boxplots, stemp
Sample Term Test 2A
1. A variable X has a distribution which is described by the density curve shown below:
What proportion of values of X fall between 1 and 6?
(A) 0.550
(B) 0.575
(C) 0.600
(D) 0.625
(E) 0.650
2. Which of the following statements about a
Sampling
U4-2
However, this may not always be the case. We need to
pay careful attention to the way we collect our samples
in order to make them useful (representative of the
population which we wish to examine).
U4-4
If our data do not fairly represent t
Sample Term Test 2A
1. A variable X has a distribution which is described by the density curve shown below:
What proportion of values of X fall between 1 and 6?
(A) 0.550
(B) 0.575
(C) 0.600
(D) 0.625
(E) 0.650
2. Which of the following statements about a
Sample Term Test 2B
1. A random variable X is described by the density curve shown below:
The probability of P (3 X 6) is equal to:
(A) 0.55
(B) 0.45
(C) 0.375
(D) 0.40
(E) 0.60
2. A random variable X follows a uniform distribution on the interval from 10
Sample Term Test Multiple Choice Answers
Question
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Sample Test 2A
A
B
A
A
B
B
B
E
D
A
B
E
A
E
C
E
B
D
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C
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A
A
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E
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E
B
Sample Final Exam 1 Part A
1. We would like to estimate the true mean amount (in $) consumers spent last year on
Christmas gifts. We record the amount spent for a simple random sample of 30 consumers
and we calculate a 95% confidence interval for to be (5
Sample Final Exam 2 Part A
1. A statistical test of significance is designed to:
(A) assess the strength of evidence in favour of H0 .
(B) assess the strength of evidence in favour of Ha .
(C) prove that H0 is true.
(D) find the probability that H0 is tru
Final Exam Solutions
Part A
1.
2.
3.
4.
5.
E
C
A
E
C
16.
17.
18.
19.
20.
E
A
D
B
B
6.
7.
8.
9.
10.
E
C
C
B
A
21.
22.
23.
24.
25.
D
A
B
C
E
11.
12.
13.
14.
15.
E
E
A
E
A
26.
27.
28.
29.
30.
E
E
C
D
D
Part B
1. (a) Let pf be the true proportion of all femal
T h e S A S S y s te m
T h e G L M
T u e s d a y , M a rc h 2 4 , 2 0 1 5 1 1 :0 2 :5 9 P M
P ro c e d u re
C la s s L e v e l In fo r m a t io n
C la s s
L e v e ls
c o n d i
3
V a lu e s
1 2 3
N u m b e r o f O b s e r v a t io n s R e a d
3 6
N u m b e
Assignment 1 Solutions
1. We have reduced the margin of error by a factor of 52 = 2.5, so we require (2.5)2 = 6.25
times the original sample size. That is, we require a sample of size 50(6.25) = 312.5
313.
2. Since this is a one-sided test with = 0.03, w
Assignment 2 Solutions
1. Since each child involved in the study is receiving only one of the two teaching methods,
there is no natural pairing between observations in the two groups. So these are two
independent samples. The ratio of the standard deviati
Unit 5 Practice Questions
1. (a) In Tim Hortons annual Roll up the Rim to Win promotion, customers who
purchase a coffee can look under the rim to see if they have won a prize. According
to the company, one out of five cups is a winner. Over the course of
Unit 5 Practice Questions Solutions
0.23 0.20
0.25 0.20
r
r
<
Z
<
1. (a) P (0.23 < p < 0.25) = P
0.20(0.80)
0.20(0.80)
100
100
= P (0.75 < Z < 1.25) = P (Z < 1.25) P (Z < 0.75) = 0.8944 0.7734 = 0.1210
0.05 0.04
(b) P (
p > 0.05) = P
Z > r 0.04(0.9
Unit 1 Practice Questions
1. We would like to estimate the true mean height of all trees in a large forest. Suppose it
is known that heights follow a normal distribution with standard deviation 6.7.
(a) What sample size is required to estimate the true me
Unit 2 Practice Questions
1. We conduct an experiment to determine whether right-handed people react more quickly
with their right hand than they do with their left hand. A machine emits a beeping sound
and a subject presses a button as quickly as they ca
Unit 4 Practice Questions
1. Hat # 1 contains one gold coin, one silver coin and one copper coin. Hat # 2 contains
two gold coins and two silver coins.
For each of the following experiments, give the complete sample space of outcomes.
(a) You randomly sel
Unit 3 Practice Questions Solutions
1. (a) We must assume that these three samples are simple random samples from their
respective populations. We must also assume that returns for each of the three
industries follow a normal distribution with common stan
Unit 3 Practice Questions
1. A stock analyst randomly selected stocks in each of three industries and compiled the
five-year rate of return for each stock. The data are shown in the table below:
mean
std. dev.
Financial Energy
10.76
12.72
15.05
13.91
8.16
Common Discrete Distributions
U7-2
U7-4
On a single trial of an experiment, suppose that there
are only two events of interest, say E and its
compliment E. For example, E and E could
represent the occurrence of a Head or a Tail on a
single coin toss, obta
Random Variables
U6-2
U6-4
For example, consider the experiment in which two
dice are tossed. Let the random variable X be defined
as the sum of the numbers showing on the two dice.
The variable X can take the values
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Ran
Central Limit Theorem
If X ~ ?(, ), then X ~& N ,
n
for large values of n (we use 30).
U9-2
U9-4
That is, regardless of the population distribution
of X, the sampling distribution of X is approximately
normal, provided that the sample size is large.
Sta
What is Statistics?
U1-1
Statistics is the set of methods for obtaining,
organizing, summarizing, presenting and analyzing
data.
Our data come from characteristics measured on
individuals or units. These can be people, animals,
places, things, etc.
The po
Unit 2 Assignment Solutions
(a)
100
There appears to be a strong
positive linear relationship
between Midterm Score and
Final Exam Score.
90
80
Final
1.
70
60
50
40
30
20
25
30
35
40
45
50
Midterm
(b)
xi
43
28
36
30
24
48
29
40
r=
(c) b1 = r
yi
92
47
80
6
Unit 1 Assignment Solutions
1.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
categorical and nominal
categorical and ordinal
quantitative
categorical and ordinal
categorical and nominal
quantitative
categorical and ordinal
2.
(a) The minimum is 0.178 and the maximum is 0.3
Variability and Randomness
U5-1
Statistics involves the study of variability. But how
can we work with something that involves so much
uncertainty?
To understand this, we consider the idea of random
behaviour.
The key lies in the fact that random behaviou
Example
Recall the coffee and sleep example:
U3-2
U3-4
Does the caffeine in coffee really help keep you
awake? Researchers interviewed 200 adults and
asked them how many cups of coffee they drink on
an average day, as well as how many hours of sleep
they