MATH 204 - SOLUTIONS 3
1.
(a)
The derivative can be obtained using the chain rule; the derivative of the term
(yi 0 1 xi )2
with respect to 0 is
2 (yi 0 1 xi ) (1) = 2(yi 0 1 xi )
whereas the derivative with respect to 1 is
2 (yi 0 1 xi ) (xi ) = 2(yi 0 1
MATH 204 - SOLUTIONS 4
1.
Given that
1 1
x1 x2
X=
T
1
xn
we have that, by the multiplication rules given
n Sx
Sx Sxx
X TX =
where
n
n
Sx =
xi
x2
i
Sxx =
i=1
i=1
The matrix inverse is computed by using the result given on the handout; a square k k matrix
McGill University Faculty of Science Department of Mathematics and Statistics April 2007
MATH 204 PRINCIPLES OF STATISTICS II SOLUTIONS
1.
(a) In an experimental study, the treatment is assigned to the experimental units by the experimenter; in an observa
MATH 204 Exercises 2: Solutions
1.
Soil.sav Analysis
(a) Under the Randomized Block Design, with soil as the blocking factor
Tests of Between-Subjects Effects
Dependent Variable: Sulphur content (ppm)
Type III Sum
of Squares
35.586(a)
Source
Corrected Mod
McGill University
Faculty of Science
April 2015
Final Examination
Principles of Statistics 2
Math 204
Monday Smarch 33rd 2015
Time: Party Time
Examiner: Dr. Fun Dude
Associate Examiner: Prof. Cool Lady
Student name (last, rst)
Wallace, Dr.
Student number
McGill University
Faculty of Science
April 2015
Final Examination
Principles of Statistics 2
Math 204
Monday Smarch 33rd 2015
Time: Party Time
Examiner: Dr. Fun Dude
Associate Examiner: Prof. Cool Lady
Student name (last, rst)
Student number (McGill ID)
I
Math 204 Practice Midterm
45 minutes
Name and McGill ID Number:
Question 1: 20 marks
You failed the midterm so your stats professor is forcing you to help run the math department disco. He wants
to know what type of music will make the disco exciting and
Outline
Building
intuition
Fundamentals of hypothesis testing
Large sample
HT of means
Large-sample test for a population mean
Small-sample
HT of means
Small-sample test for a population mean
p-values
Large-sample
HT of
p-values
proportions
Examples
Large
Outline
Properties of
continuous
distributions
Uniform
Properties of continuous distributions
Uniform distribution
Distribution
Normal
istribution
Using the table
Standardizing
Examples
Reversing the
problem
Normal
approximation to the
Binomial
Assessing
Outline
Large sample
Throughout this chapter, we write CI for condence interval.
CI for
Interpretation
The topics to be discuss are as follows:
Examples
Small sample
CI for
More
examples
Large sample
CI for p
Sample size
calculations
Large-sample CI for
Outline
Samples vs
Population
Population versus sample
Sample
statistics
Properties of
X
Expectation and variance of X
Distribution of X
Central Limit
Theorem
Central Limit Theorem
Simulated
example
Theoretical
example
More
examples
Examples
Putting it al
Outline
Random
variables
Discrete vs
Random variables
continuous
Discrete vs continuous
Discrete
probability
distributions
Examples
Probability distributions for discrete random variables
Bernoulli distribution
Bernoulli
distribution
Binomial
distribution
Non-parametric tests summary
Method
One-way
Chi-squared
Two-way
Chi-squared
Sign
MannWhitney
Wilcoxon
Signed Rank
KruskalWallis
Friedman
When do we use it?
One-way multinomial (count) data.
e.g. test if each of k outcomes
equally likely.
Two-way multinomi
MATH 204: P RINCIPLES OF S TATISTICS 2
W INTER 2015
Instructor :
Email :
Ofce Hours :
Teaching Assistant :
Tutorials :
Ofce Hours :
Textbook :
Michael Wallace (Purvis 16)
[email protected]
Tuesdays 3pm-4pm; please email in advance if possible
Meng
Tutorial 11 Problems
1. Under what circumstances is the sign test preferred to the t-test for making inferences about
the central tendency of a population?
2. What is the probability that a randomly selected observation exceeds the
a) Mean of a normal dis
100 points total
Midterm Exam for MATH 204: Winter 2012
Instructor: Russell Steele
1. (20 pts) Professor Steeles brother works as a cook in an Italian restaurant. His brother uses a certain
brand of canned tomatoes for sauces. He is worried that the varia
100 points total
Midterm Exam for MATH 204: Winter 2012
Instructor: Russell Steele
1. (20 pts) Professor Steeles brother works as a cook in an Italian restaurant. His brother uses a certain
brand of canned tomatoes for sauces. He is worried that the varia
Exercises: ANOVA and Multiple Comparisons
Here are a few exercises to work on in your spare time. The
first is an example from the Handout file: first try and do it
without referring to the Handout (but feel free to refer to the R
tutorial material).
Next
Math 204 Assignment 1
Deadline: 11.59pm, Sunday 14th February, 2016
Submit via myCourses
Grade Expectations
Following the final exam of one of my previous courses, I investigated whether there was any relationship between the year group to which a student
Math 204 Assignment 2
Deadline: 11.59pm, Sunday 13th March, 2016
Submit via myCourses
Statistics gets my heart racing
At the start of this year I bought an activity tracker. Worn on the wrist, it automatically logs various
pieces of information about my d
Math 204 Assignment 3
Deadline: 11.59pm, Sunday 3rd April, 2016
Submit via myCourses
Heart rate limiting steps
Exciting news! Following your excellent work analyzing the heart rate data of a statistics professor,
you have secured funding to expand your wo
Chapter 3
The language of probability
Outline:
Denitions
Events, sample spaces and probability
Basics of set
theory
Probability
Basics of set theory
and sets
Relationship of probability to set theory
Conditional
Conditional probability
probability
Indepen
Quantitative vs qualitative data
Quantitative
data
Notation
Summarizing
Quantitative Data
Dot plots
Histograms
Quantitative data are numerical in nature
Examples: blood pressure, temperature, distance,
speed, counts, etc.
Qualitative data are categorical
Welcome to MATH 203
What to expect
Introduction
What is
statistics?
Welcome to MATH 203 (Principles of Statistics I).
Fundamentals
The course will meet Monday, Wednesday, Friday from
Collecting
Data
8:35 AM 9:25 AM.
Confounding
Sampling and Bias
Summarizi
MATH 204 - ASSIGNMENT 2: S OLUTIONS
Although the original data indicate a non-linear relationship of FEV with height, and potentially complicated modelling, a log transformation of the response, yields a fairly simple linear relationship (see
Figure 1), a
MATH 204 - SOLUTIONS 1
The data yield the following statistics:
Treatment
Sample Size
Sample Mean
Sample Variance
1.
ni
xi
s2
i
0
4
26.75
28.92
2
5
33.60
20.30
4
5
38.20
22.70
For the three two sample t-tests:
(a)
Groups 0 vs 2:
s2
P
=
1
1
(n1 1)s2 + (n2
MATH 204 - ASSIGNMENT 1: S OLUTIONS
1. To compute the ANOVA-F statistic, we rst need various quantities that are available from the data
given: we have k = 4 and n = 4 35 = 140, and
x =
s2
P
=
1
n
ni
k
xij =
i=1 j=1
1
nk
1
140
4
(ni xi ) = 11.315
i=1
k
(n
MATH 204 - SOLUTIONS 1
1.
We have
k
ni
ni
k
SS =
(xij x)
2
(xij xi + xi x)2
=
i=1 j=1
i=1 j=1
k
=
ni
i=1
j=1
k ni
=
i=1
(xij xi )2 + 2(xij xi )(xi x) + (xi x)2
2
(xij xi )
j=1
k
+
i=1
k
+2
i=1
ni
(xi x)2
j=1
ni
j=1
(xij xi )(xi x)
Now
k
i=1
k
i=1
ni
(xij
Analysis of Variance: Key points
Terminology:
I
Designed vs. observational studies.
I
Response, factor, factor level, treatment, experimental unit.
I
Completely randomized designs.
Analysis of Variance
173
Analysis of Variance: Key points
One-way ANOVA:
I