HE104A - STATISTICAL THEORY AND METHODS
Tutorial 8
1. Random samples from two normal populations produced the
following statistics:
2
s1
= 60
n1 = 20
s2
2
;
= 25
n1 = 20
Can we infer at the 5% significance level that the
variance of population 1 is larger
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 10
1.
The term regression was originally used in 1885 by Sir
Francis Galton in his analysis of the relationship between the
heights of children and their parents. He formulated the law
of
universal
regressi
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 7 (to be discussed on 16 March):
Topics: AS-AD
If you are using 10th edition textbook, they are
1.
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 1 (to be discussed on 27 Jan):
Topics: Introduction to Macroeconomics
1. Question 9, page 159.
(Hi
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 2 (to be discussed on 3 Feb):
Topics: Aggregate Expenditure and Equilibrium Output
1. Question 7,
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 3 (to be discussed on 10 Feb):
Topics: Government and Fiscal Policy
1. Question 7, page 201, 9th e
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 4 (to be discussed on 17 Feb):
Topics: Money Supply
1. Question 15, page 243, 10th edition; not av
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 5 (to be discussed on 24 Feb):
Topics: Money Demand and Equilibrium Interest Rate
1. Question 1, p
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 6 (to be discussed on 9 March):
Topics: Equilibrium in Goods and Money Market
If you are using 10t
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 8 (to be discussed on 23 March):
Topics: Labor Market and Unemployment
If you are using 10th editi
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 9: (to be determined)
Topics: The Debates in Macroeconomics and long-run economic growth.
1. Quest
HE1002 Principles of Macroeconomics Semester 2, 2011-12
Textbook: Karl E. Case, Ray C. Fair and Sharon Oster, Principles of Macroeconomics, 10th E.
Tutorial 10 (answers to be released on 6 April):
Topics: The Open Economy.
1. Refer to Table 1 and Assumpti
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 7
1. A random sample of size 20 from a normal population gave x =
23 and s = 9. Can we infer at the 5% level of significance
that the population mean is greater than 20?
2. A random sample of size 10 from a
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 6
1. In a random sample, 86 of 500 persons given a certain
vaccine experienced some discomfort. Construct a 95%
confidence interval for the true proportion of persons who
will experience some discomfort fro
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 5
1. A vending machine is set so
dispensed is a random variable
standard deviation of 15 ml.
that the mean amount dispensed
36 is not more than 204 ml.
that the amount of drink
with a mean of 200 ml and a
D
3. DISCRETE PROBABILITY
DISTRIBUTIONS
3.1 Bernoulli Distribution
A Bernoulli r.v. is a discrete r.v. X where
P(X = 1) = p and P(X = 0) = q = 1- p.
Then,
E(X) = 0(q) + 1(p) = p
V(X) = (0 - p)2q + (1 - p)2p
= p2q + q2p
= pq .
3.2 Binomial Distribution
A b
4. CONTINUOUS DISTRIBUTIONS
4.1 Probability Density Function
The probability distribution of a continuous
r.v. is known as the probability density
function (pdf).
The pdf may be represented by a formula or
graphically by a smooth curve.
Let f(x) be the
5. SAMPLING DISTRIBUTIONS
5.1 Introduction
In real life, populations are very large and
the parameters are unknown.
Instead
of
investigating
the
whole
population, a random sample is taken from
the population, calculate a sample statistic
related to the
6. INTRODUCTION TO INFERENCE
6.1 Concepts of Estimation
Statistical inference is the process where we
get information about populations from
samples.
The two procedures for making inferences
are:
1) estimation
2) hypothesis testing.
The aim of estimati
7. HYPOTHESIS TESTING I
7.1 Inference About When is Unknown
Recall that when is known X is normally
distributed:
- if sampling is from a normal population, or
- if the population is not normal but n is large.
When is unknown, replace it by its point
est
8. HYPOTHESIS TESTING II
8.1 Tests Concerning Variances
Make inferences about the ratio of two
population variances.
The point estimator of 12/22 is S12/S22 .
If we have independent random samples
from two normal populations, then the
statistic [S12/12
10. SIMPLE LINEAR REGRESSION
AND CORRELATION
10.1 Introduction
Regression
analysis
examines
the
relationship among the variables.
Can be used to predict the value of one
variable (the dependent variable) based on
the value of other variables (the indepe
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 1
1. The following data set shows the number of issues of a
particular monthly magazine read by 25 people in a year.
Summarise the data set in whatever way you think is
appropriate.
0, 0, 1, 0, 0, 2, 11, 0,
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 2
1. The trustee of a companys pension plan has obtained the
employees feelings towards a proposed change in the plan.
The table below shows the breakdown of the responses.
Decision
For:
Against:
Managers
9
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 3
1. If the r.v. X has a binomial distribution with n = 10 and
p = 0.4, find the following probabilities:
(a)
(b)
(c)
P(X = 3)
P(X < 6)
P(X 7)
2. The number of calls received at a certain switchboard
betwee
HE104A - STATISTICAL THEORY AND METHODS
Tutorial 4
1. The probability density of the r.v. X is given by
f(y) =
=
(y + 1)/8
0
for 2 < y < 4
elsewhere
Find P(Y < 3) and P(2.5 < Y < 3.5).
2. A restaurant receives a delivery each morning at a time
that varies
1.1 Introduction to Statistics
Statistics is a field of study that is
concerned with getting information from
data.
Data may be qualitative or quantitative.
Qualitative
data
are
categorical
observations (e.g. marital status of
employees).
Quantitative