Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Intro to the course
Descriptive statistics
This time:
Group exercise about sampling variation
Probability
September 15, 2015
1 / 19
Exercise: population versus sample
Split into groups of 4 or 5
One person in each group write down heig
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Hypothesis testing about one parameter (Chapter 9)
Today:
Hypothesis testing about the dierence between two parameters
(Chapter 10)
1 / 18
Motivation
There are two populations: X and Y .
2
X fX (x) with mean X and variance X
2
Y fY (y
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Begin talking about continuous RV
Today
Finish talking about continuous RV
1 / 27
Expectation of continuous RV
Last time we talked about taking expectations of functions of continuous
RV
E [g (X )] =
x
g (x)f (x)dx
We can get the mean
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Population: the complete set of all items that interest an investigator.
Sample: an observed subset (or portion) of a population with sample size given by n.
Parameter: a numerical measure that describes a specific characteristic of a population.
Statisti
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Econ 2222A
September 18, 2015.
Practice problems, week 1.
1. The following table lists a sample of daily temperatures (in Celsius) in London, Ontario. Each month
from January to December has been sampled one time.
JAN
6.3
FEB
5.5
MAR
0.3
APR
6.3
MAY
13
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Econ 2222A
September 18, 2015.
Practice problems, week 2.
1. Prove both the complement rule and the addition rule.
2. Are A and A independent? Why or why not?
3. Prove that, if events A and B are independent, P (AB) = P (A).
4. A1 , . . . , Ak and B1 , .
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Econ 2222A
Solutions to Practice problems, week 2.
1. In the lecture notes.
2. P (A A) = 0, while P (A)P (A) = 0 if P (A) (0, 1).
3. If A, B independendent, then P (A B) = P (A)P (B). We know from the denition of conditional
(AB)
probability that P (AB)
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Midterm 2
Econ 2222A
November 11, 2015, 7:159:15pm
Instructions:
Show your work
Express numeric answers in either decimal form or simplied (that is, reduced)
fraction form. Nonreduced fractions may be marked as incorrect.
Use of only nongraphic (i.e
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
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Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Final Exam
Econ 2222A
December 10, 2014, 25pm
Instructions:
Show your work
Express numeric answers in either decimal form or simplied (that is, reduced) fraction form. Nonreduced fractions may
be marked as incorrect.
Use of only nongraphic (i.e. non
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Start hypothesis testing
Today:
Continue hypothesis testing
Next time:
Instructor evaluations will happen at the beginning of next class
(Thursday, Nov 26)
It is a very important form of feedback to me and the department. I
enjoy teach
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Continue hypothesis testing for one population parameter
Today:
Finish hypothesis testing for one population parameter
1 / 23
Test of Mean of Normal: Variance Known
Say we want to test a hypothesis of the mean of a normally distributed
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Estimation and condence intervals for the dierence between two
population parameters
Today:
Finish estimation and condence intervals for dierences between two
population parameters
Similarity of T  and Z based condence intervals
Bern
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Intermediate Econometrics 1
Economics 2222A
Professor Nirav Mehta
University of Western Ontario
September 10, 2015
September 10, 2015
1 / 61
Why learn statistics?
Question: Is it more eective to take notes on the laptop or by hand?
66 students were assign
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Last time
Probability
basic outcomes
events
Today:
Interpretations of probability
Postulates and rules of probability
Counting
Conditional probability
Bivariate probability
Independence
Bayes theorem
1 / 40
What is probability?
We will discuss three inter
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Discrete random variables
Probability distribution function
Cumulative distribution function
Expected value
Today
Discrete random variables
Expected value
Variance of discrete RV
Mean and variance of linear functions of RV
Bernoulli, B
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Discrete random variables
Poisson RV
Jointly distributed discrete RV
Today:
Discrete random variables
Jointly distributed discrete RV
1 / 15
Conditional mean and variance
Recall we can write the conditional distribution of y given X as
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Discrete random variables
Expected value: E [X ]
Expected value of a function of a RV X : E [g (X )]
Variance
Mean and variance of linear functions of RV
Specic distributions
Bernoulli RV
Binomial RV
Today:
Discrete random variables
Po
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Finish talking about continuous RV
Today
Talk about distributions of sample means
1 / 44
Motivation: Keep your eyes on the prize
Our objective is to say something about the real world.
Here are some questions of policy interest:
Does p
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Talk about distributions of sample means
Today
Finish talking about distributions of sample means
Group exercise
1/9
Review from last time 1
The sample mean X is a RV with a mean and a variance.
Mean, or expectation, of the sample mean
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Talk about distributions of sample means
Today
Finish talking about distributions of sample means
Group exercise
1/9
Review from last time 1
The sample mean X is a RV with a mean and a variance.
Mean, or expectation, of the sample mean
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Estimation
Condence intervals
Today:
Condence intervals, specic examples
1 / 14
Condence intervals
We want to make a statement about some population parameter based
on information from a random sample
To do this, we use an estimator
a
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Finish discussing the distribution of the sample mean.
Work through some examples in groups.
Ill put the answers online next week.
Today:
Estimation
Condence intervals
1 / 27
The point
Keep in mind our objective: draw inferences about
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Estimation and Condence intervals for one population parameter
Today:
Estimation and Condence intervals for the dierence between two
population parameters
Normal pop
Bernoulli pop
1 / 25
Instead of estimating just one parameter, someti
Western University (Ontario)  Also known as University of Western Ontario
ECONOMICS 2222

Fall 2015
Overview
Last time:
Finish talking about continuous RV
Today
Talk about distributions of sample means
1 / 44
Motivation: Keep your eyes on the prize
Our objective is to say something about the real world.
Here are some questions of policy interest:
Does p