Clicker Question
Below is a list of variables collected from an annual
survey of university students.
Variables that take numeric values may be classified as
discrete or continuous.
Which variable is discrete?
A)
Monthly rent for student accommodation
(in
Clicker Question
Some samples each with sample size 8 are:
1.
1
2
3
4
5
6
7
8
2.
1
1
1
1
8
8
8
8
3.
1
1
3
3
6
6
8
8
Each sample has the same mean and the same range.
Inspect the samples and, without doing any calculation,
arrange the samples by the magnit
ECONOMICS 325
Section 2 Exam B
Mid-term Exam
Oct 9, 2014
Winter 2014/15
2:00 to 3:15 PM
Total points = 35
Question 1 State whether each of the following claims is True or False.
To get points you must clearly explain your answer with an equation or exampl
ECONOMICS 325
Section 2 Exam A
Mid-term Exam
Oct 9, 2014
Winter 2014/15
2:00 to 3:15 PM
Total points = 35
Question 1 State whether each of the following claims is True or False.
To get points you must clearly explain your answer with an equation or exampl
ECONOMICS 325
Section 1 Exam B
Mid-term Exam
Oct 9, 2014
Winter 2014/15
12:30 to 1:45 PM
Total points = 35
Question 1 [5 points] Let A be the event a student wears a blue shirt and B be the
event a student wears blue shoes. Probabilities are: P(A)=0.4 , P
ECONOMICS 325
Section 1 Exam A
Mid-term Exam
Oct 9, 2014
Winter 2014/15
12:30 to 1:45 PM
Total points = 35
Question 1 A data set has 253 daily observations on closing prices (prc) for the
company WOW and a market index (Spindex). Stata results for summary
Chapter 9.1
Hypothesis Testing
To test the hypothesis, a test statistic is computed from the sample
data. The decision to take can then be either:
Interval estimation leads the way to hypothesis testing.
do not reject the null hypothesis, or
A statistica
Testing the Equality of Variances
Textbook Reference: Chapter 10.4
Like the chi-square distribution, the F distribution is defined only for
non-negative values and the skewed shape of the probability density
function depends on the degrees of freedom.
Con
Working with a Sample Proportion
Textbook References (8th Edition):
Chapter 6.3 Sampling Distribution of a Sampling Proportion
Chapter 7.4 Confidence Intervals for the Population Proportion
Chapter 7.7 Sample Size Determination: Population Proportion
The
Chapter 5
The probability density function (PDF) is given by:
Continuous Random Variables
f( x ) 0
A continuous random variable can take any numerical value in some
interval. Assigning probabilities to individual values is not possible.
Probabilities can
Chapter 4.1
Random Variables
A random variable is a variable that takes on numerical outcomes
defined over a sample space of a random experiment.
A random variable has a probability distribution.
Chapter 4.2
Discrete Random Variables
For a discrete random
Chapter 3.1
Random Experiment, Outcomes and Events
In the analysis of economic data any conclusions involve some
uncertainty. To incorporate ideas of uncertainty into the study of
economic data an understanding of probability theory is needed.
the empty s
Chapter 7.1
Properties of Point Estimators
Let the random sample X 1 , X 2 , . . . , X n be a set of random
variables that are independently and identically distributed.
An applied study works with a data set.
The numeric observations are: x 1 , x 2 , . .
Chapter 6
Sampling and Sampling Distributions
A sample of data are the observed numerical outcomes
x 1 , x 2 , . . . , x n (lower case notation).
The sample mean can be calculated as:
A random sample is a set of random variables
X 1 , X 2 , . . . , X n (u
Lecture Notes for Economics 325
Introduction to Empirical Economics
(Probability and Statistics for Economists)
Diana Whistler
Vancouver School of Economics
Copyright by Diana Whistler
All Rights Reserved.
These course materials may be downloaded for stud
Clicker Question
Consider the following samples for two variables X and Y.
X
1
2
3
4
5
Y
6
3
1
3
8
X
1
2
3
4
5
Y
18
16
10
3
3
X
1
2
3
4
5
Y
2
4
10
18
28
1.
2.
3.
Inspect the data and, without doing any calculation, pick the
sample with negative covariance
Clicker Question
From the Statistics Canada census for the year 2011
it was found that:
13% of people in Canada lived in British Columbia;
4% of people in Canada were of Chinese ethnic origin;
10% of people living in British Columbia were of Chinese
ethni
Clicker Question
From the Statistics Canada census for the year 2011
it was found that:
13% of people in Canada lived in British Columbia;
4% of people in Canada were of Chinese ethnic origin;
10% of people living in British Columbia were of Chinese
ethni
Econ 325 Section 003
Notes on Mathematical Expectation, Variance, and Covariance
By Hiro Kasahara
Mathematical Expectation: Examples
Consider the following game of chance. You pay 2 dollars and roll a fair die. Then
you receive a payment according to the
Econ 325 Section 003
Notes on Bernoulli Random Variable and Binomial Distribution
By Hiro Kasahara
Bernoulli Random Variable
Consider a random variable X that takes a value of zero or one with probability 1 p and
p, respectively. That is,
0 with prob. 1 p
Clicker Question
A university instructor compares the mid-term exam grades
and the final exam grades for a course.
95% confidence interval estimates for the mid-term grade
average and the final grade average are calculated.
The results show that the two c
Clicker Question
For a sample of daily stock market prices for a company a
financial analyst would like to test the null hypothesis that
the population mean of the daily returns is zero against the
alternative of negative mean returns.
For the sample the
Clicker Question
Is the next statement True or False?
With a sample of data, the sample proportion is at the
center (midpoint) of an interval estimate for a
population proportion.
A)
B)
-1-
True
False
Econ 325 Sample Proportion
True.
Note: with a sample o
Clicker Question
Is the next statement True or False?
If a null hypothesis is rejected against an alternative at the
5% level, then using the same data, it must be rejected
against the alternative at the 1% level.
A)
True
B)
False
-5-
Econ 325 Chapter 9
F
Clicker Question
A Statistics Canada study Sugar consumption among
Canadians of all ages found that, for a sample of Canadians in
2004, the average daily intake of sugar was 111.5 grams.
A 95% confidence interval estimate was from 109.9 to 113.1.
Which st
Clicker Question
For a sample of final grades for 10 students the average
grade is 75.
A 90% interval estimate for the population mean is
calculated. The upper limit is 77.
Find the lower limit of the interval estimate.
A)
68
B)
70
C)
71
D)
73
E)
75
-4-
E
Clicker Question
Final grades for a university course follow a normal
distribution with mean 75.
Ten (10) percent of students get a grade of 80 or above.
Find the standard deviation of final grades
(round to the nearest integer).
A)
2
B)
4
C)
5
D)
10
- 13
Clicker Question
Final grades for a university course follow a normal
distribution with mean 75.
The range of grades between 70 and 80 includes 80% of all
students in the course.
For a random sample of two students the probability that the
average of thei
Clicker Question
Consider a binomial experiment with n = 5 trials.
A trial has one of two outcomes: success or failure; where
the probability of a success is p.
Suppose the first two trials are both successes.
Which statement is correct?
A)
the probabilit
ECON 325
Assignment 2
Part I:
This report analyzes daily stock market data for the Goodyear Tire & Rubber
company in the year 1999. From the simulation experiment the percentage difference
between the true population mean and the average of the sample mea
ECON 325
Assignment 1
Summary statistic for Daily Returns (in percent)
Mean
Standard Deviation
Goodyear Tire & Rubber
-.1948123
2.369696
CRSP
.0929861
1.072555
Summary Statistics for Closing Prices
Mean
Goodyear Tire
& Rubber
S&P 500
Index
Standard
Deviat
SamplingDistributionoftheSampleVariance
TextbookReference:Chapter6.4
Lettherandomsample X 1 , X 2 ,., X n beasetofidentically
distributedandindependentrandomvariableswithmean and
E s 2X
Aresultis:
Thiscanbeshownasfollows.
n
n
2
E ( X i X )2 E ( X i )