Carleton University
Department of Economics
ECON 2202 E
Statistical Methods in Economics and Business II
Fall 2015
Professor Ba Chu
Class: Tuesdays and Thursdays, 1:05 - 2:25 p.m.
Tutorial: Thursdays, 11:35 - 12:55 p.m. (details: TBC)
Office: Loeb Buildin
Type A Questions
1. (30 marks) It is well known that the key to estimating and testing the dierence between two population
means 1 2 from two samples is to nd an appropriate statistic. However, the appropriate statistic
depends on the types of two samples
ECON 2202 E
FALL 2014
Statistical Methods in Economics and Business I
TEST 1A
This test is worth a total of 75 marks with marks per question as indicated.
Unless otherwise specified assume all populations are normally distributed.
For full marks, show you
1. A major U.S. oil company has developed two blends of gasoline. Managers are interested
in estimating the difference in mean gasoline mileage that will be obtained from using the two
blends. As part of their study, they have decided to run a test using
Topic 12
Analysis of Variance
1
General ANOVA Setting
We have so far learned of ways to test the validity of hypotheses for
single and two population situations.
It is frequently necessary or desirable to compare more than two
population means.
For exampl
ECON 2202 TUTORIAL 1 TOPIC 10
State the hypotheses, critical values, decision rules, calculate the test statistics, and state the
conclusions for the following.
Sample 1 has a variance of 2.54 and a sample size of 4. Sample 2 has a variance of 3.60 and a
ECON 2202 Statistical Methods in Economics and Business II
PRACTICE ASSIGNMENT - TOPIC 13
SHORT-ANSWER QUESTIONS
1. In using the chi-square goodness-of-fit test, a statistician needs to make certain that
none of the expected frequencies are less than what
ECON 2202 Statistical Methods in Economics and Business II
Solutions PRACTICE ASSIGNMENT TOPIC 12
SHORT-ANSWER QUESTIONS
1. You must test: H0: 1 = 2 = 3 = 4. You draw 8 observations from the first population, 9
from the second, 12 from the third, and 11 f
Topic 15
Multiple Regression Analysis and Model Building
1
The Multiple Regression Model
Model with Two or More Independent Variables
2
Regression Analysis
Again regression analysis is used to:
Describe the impact of changes in independent
variables on th
USING EXCEL FOR TOPICS
10,11,12,14, and 15
DESCRIPTIVE STATISTICS
Note that Excel has various
functions which can also be used
to calculate individual statistics.
F TEST FOR PAIR OF VARIANCES
Note that Excel only performs only a one tail test.
To get the
ECON 2202 Statistical Methods in Economics and Business II
PRACTICE ASSIGNMENT - TOPIC 15
SHORT-ANSWER QUESTIONS.
1. A recent study by the U.S. Department of Agriculture attempted to develop a multiple regression model to explain
variation in farm income.
ECON 2202 Statistical Methods in Economics and Business II
Solutions PRACTICE ASSIGNMENT - TOPIC 15
SHORT-ANSWER QUESTIONS.
1. A recent study by the U.S. Department of Agriculture attempted to develop a multiple regression model to explain
variation in fa
ECON 2202 TUTORIAL TOPIC 12
1. Consider the following partial ANOVA table.
Source
Between
Samples
Within Samples
Total
a.
b.
c.
d.
SS
1,745
df
MS
F
240
246
6,504
How many populations are being considered?
Complete the ANOVA table.
Test the equality of mea
ECON 2202: Statistical Methods in Economics and Business II
Lecture 6: Estimation and Hypothesis Testing for Two
Population Parameters (V) (Chapter 10)
Estimation and Hypothesis Tests for Two Population Proportions
1
Introduction
So far, we have introduce
ECON 2202: Statistical Methods in Economics and Business II
Lecture 1
Welcome to ECON 2202: Statistical Methods in Economics and Business II.
We have two things to do in this lecture: one is to talk about the course outline; the
other is to give you a big
ECON 2202: Statistical Methods in Economics and Business II
Lecture 5: Estimation and Hypothesis Testing for Two
Population Parameters (IV) (Chapter 10)
Interval Estimation and Hypothesis Tests for Two Population Means Using
Paired Samples
1
Introduction
ECON 2202: Statistical Methods in Economics and Business II
Lecture 23: Introduction to Linear Regression and Correlation Analysis (IV)
Simple Linear Regression Analysis (III)
1
How to test linear relation for two variables?
1.1
The three types of tests
W
ECON 2202: Statistical Methods in Economics and Business II
Lecture 25: Introduction to Linear Regression and Correlation Analysis (VI)
Multiple Regression Analysis and Model Building (II)
1
Introduction
We introduced three equivalent types of tests about
Solution to Practice Problem Set 4
1. (Problem 14-2 on page 567.)
(a) The scatter plot is shown as follows:
Sc att er Plo t
2 50
2 00
y Va riable
1 50
1 00
50
0
0
5
10
15
20
25
x Var iable
Based on the scatter plot, there appears to be a fairly strong pos
ECON 2202: Statistical Methods in Economics and Business II
Lecture 11: Goodness-of-Fit Tests and Contingency Analysis (II)
Goodness-of-Fit Tests (II) (Chapter 13)
1
Introduction
In the last lecture, we introduced the idea how to use the goodness of fit t
1. (20 Marks) We have introduced four famous statistics: 2 and up to Chapter
11. It is well known that the two statistics, and are introduced mainly for
interval estimations and hypothesis testing of population mean(s) and population
proportion(s).
(a) (6
ECON 2202: Statistical Methods in Economics and Business II
Lecture 3: Estimation and Hypothesis Testing for Two
Population Parameters (II) (Chapter 10)
Estimation for Two Population Means Using Independent Samples
1
Estimating the dierence 1 2 when at le
Sample of final exam
This question paper has 10 pages: five pages of questions, five pages of tables (one ,
one , one 2 two s).
Part A (For all sections A, B, and C)
1. (10 marks) Suppose three populations 1 2 3 are normally distributed with means
1 2 and
ECON 2202 Statistical Methods in Economics and Business II
Solutions PRACTICE ASSIGNMENT - TOPIC 13
SHORT-ANSWER QUESTIONS
1. In using the chi-square goodness-of-fit test, a statistician needs to make certain that
none of the expected frequencies are less
ECON 2202 TUTORIAL TOPIC 14
1. A random sample of variables, x and y, produced the following results.
x
19
13
17
9
12
25
20
17
Y
7
9
8
11
9
6
7
8
a. Draw the scatter diagram and comment on the relationship.
b. Calculate the correlation coefficient. (x = 1
ECON 2202 TUTORIAL TOPIC 11
1.
Sample mean
Sample standard deviation
Sample size
Group 1
195
35.10
120
Group 2
216
37.8
135
a. Assuming the population variances are equal, construct a 90% confidence interval for the
difference in the means which measure t
ECON 2202 Statistical Methods in Economics and Business II
Solutions PRACTICE ASSIGNMENT - TOPIC 11
Unless otherwise specified assume all populations are normally
distributed and independent.
SHORT-ANSWER QUESTIONS
1. State the formula used to test for th
Topic 13
Analysis of Categorical Data:
Tests of Independence and
Goodness of Fit
1
Tests of Independence - Contingency Analysis
Contingency Tables classify data making it qualitative
A table used to classify sample observations according to two or
more id
Topic 11
Estimation and Hypothesis Testing of Differences
between Two Population Means and Proportions
(Textbook Chapter 10)
1
Difference of two population means
2
Two Possible Sample Types
Independent Samples
Paired or Dependent Samples
3
Independent Sam
2202 FINAL EXAM REVIEW SUMMARY AND REMINDERS
TOPIC 10
Hypothesis tests
Single variance Chi square test
Be sure to know how to read the tables
Two variances F test
Be sure to know how to read the tables
Remember use the upper tail test and know the ru
Topic 10
Hypothesis Tests for One and Two
Population Variances
(Textbook Chapter 11)
1
Steps for Hypothesis Testing
Step 1: Define the Null and Alternate hypotheses.
Step 2: Find the critical value from the tables. Draw the
distribution and indicate rejec
ECON 2202 Statistical Methods in Economics and Business II
PRACTICE ASSIGNMENT - TOPIC 12
SHORT-ANSWER QUESTIONS
1. You must test: H0: 1 = 2 = 3 = 4. You draw 8 observations from the first population, 9
from the second, 12 from the third, and 11 from the
ECON 2202 Statistical Methods in Economics and Business II
PRACTICE ASSIGNMENT TOPIC 10
Unless otherwise specified assume all populations are normally
distributed.
SHORT-ANSWER QUESTIONS
1. Dr. ABC is an economist who studies the effects of immigration. H
ECON 2202 Statistical Methods in Economics and Business II
PRACTICE ASSIGNMENT TOPIC 14
SHORT-ANSWER QUESTIONS
1. In regression, what is the value of y y measure and what is it called?
2. What are data points that lie apart from the rest of the points cal
ECON 2202 Statistical Methods in Economics and Business II
Solutions PRACTICE ASSIGNMENT - TOPIC 10
Unless otherwise specified assume all populations are normally
distributed.
SHORT-ANSWER QUESTIONS
1. Dr. ABC is an economist who studies the effects of im