Department of Management, UTSC
MGEB12 Quantitative Methods in Economics II L01/L30
Assignment #1 Winter 2015
Due TUE/WED January 27/28 in class. Late Assignments will not be accepted. This assignment is
worth 2.5% of your final mark.
You can work individu
MGEB12 Lecture 4
Hypothesis Testing about two Population
Means
Ata Mazaheri
1
Lecture Outline
Inferences About the Difference Between
Two Population Means: 1 and 2 Known
Inferences About the Difference Between
Two Population Means: s 1 and s 2 Unknown
2
MGEB12 Lecture 2
Confidence Interval
Hypothesis Testing of the Mean
(Variance Unknown)
Ata Mazaheri
1
Lecture Outline
So Far!
Confidence Interval
Population Mean: Unknown
Problem Solving
2
Confidence Interval
Margin of Error and the Interval Estimate
A po
MGEB12 Lecture 3
Confidence Interval/Hypothesis Test
of Proportions
Type II Error
Ata Mazaheri
1
Lecture Outline
Population Proportion
Type II Error:
 Calculating the Probability of Type
II Errors
 Determining the Sample Size for a
Hypothesis Test Abo
MGEB12 Lecture 1
Review
Hypothesis Testing of Mean (Variance
Known)
Ata Mazaheri
1
Lecture Outline
A Short Review
Developing Null and Alternative
Hypotheses
Type I and Type II Errors
Population Mean: Known
Population Mean: Unknown (Next
Session)
2
Sa
Department of Management, UTSC
MGEB12 Quantitative Methods in Economics II L01/L02  Assignment #2 Solution
Problem 1
(a)
H0: = 606.40
Ha: 606.40
RejectH0ifZ0  Z/2 or Z0 Z/2,
x 0 x 606.40
Z0
/ n
65 / 30
P[Z Z/2 ] = /2 get P[Z Z0.025 ] = .025 get Z0.025
= mean of x = standard deviation of x =
Population
Conclusion from
Test
H0 True
Correct
Conclusion
Type I Error
Accept H0
Reject H0
Ho: 0
Ha: < 0
Summary of test for
population mean
variance unknown (ttest)
Manufacturers claim starts w/ H0 (,=);
Ha True
Testing of population mean, population variance known Summary
Test Statistic
P[Z Z ] = , P[Z Z/2 ] = /2
CI:
x 0
x Z /2
Z0
n
/ n
If using pvalue approach, reject H0 if pvalue
Tests
Ho: 0
Ha: < 0
Reject Ho if
Z0  Z
P[Z Z0]
Ho: 0
Ha: > 0
Reject Ho if
Z0
MGEB12 Lecture 3
Confidence Interval/Hypothesis Test of
Proportions
Type II Error
Ata Mazaheri
0
Lecture Outline

Population Proportion
Type II Error:
Calculating the Probability of Type II Errors
Determining the Sample Size for a
Hypothesis Test About a
MGEB12 Quantitative Methods in Economics II
Lecture 01 Introduction
Statistics is the science of the collection, organization,
and interpretation of data
G. Hopkins quoted by Wikipedia
Collection
Summaries (graphical / numerical),
What
happened?
Trivia
MGEB12 Lecture 5
Match Sample Design;
Hypothesis Testing about Two
Proportions
Towards Inference about Population
Variance
Ata Mazaheri
1
Lecture Outline
Inference
about two Population Means, Variance
Unknown (Review)
Inferences About the Difference Bet