Data is a set of numeric observations.
Sources of data:
Government statistical agencies (Statistics Canada)
Stock market activity
Statistical methods can be used to summarize the information in
Chapter 10.1 Tests of the Difference Between Two Means
Interval estimation for the difference between two population means was presented in the lecture notes for Chapters 8.1 and 8.2. An extension to hypothesis testing is of interest for applied work. For
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. Population characteristics are summarized by parameters the true values are typically
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.
A random variable can be denoted by X (upper-case) and a po
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.
A random ex
Chapter 10.4 Testing the Equality of Variances
Consider two random samples. Assume:
independent samples, and
normally distributed populations.
The samples have n x and n y observations and the population
variances are X and Y .
Estimators of the pop
Interval estimation leads the way to hypothesis testing.
A statistical hypothesis is an assumption about the behaviour of a
A statement of the hypothesis must be formed.
The null hypothesis is denoted by H0 (H-na
Chapter 9.5 Measuring the Power of a Test
An economic problem motivates the statement of a null and
For a numeric data set, a decision rule can lead to the rejection of the
null hypothesis. This involves the risk of making an error
Confidence Intervals for the Difference
Between Two Population Means
Let ( X i , Yi ) for i = 1, 2, . . . , n be a pair of random variables that
each follow the normal distribution with population means
X and Y .
This set-up is called matched
Continuous Random Variables
A continuous random variable can take any numerical value in some
interval. Assigning probabilities to individual values is not possible.
Probabilities can be measured in a given range.
For a continuous random variabl
Sampling and Sampling Distributions
A random sample is a set of random variables
X 1 , X 2 , . . . , X n (upper case notation) that are:
That is, each of these random variables has mean and
variance ; and
Chapter 6.4 The Sample Variance
Let the random sample X 1 , X 2 , . . . , X n be a set of identically
distributed and independent random variables with mean and
The sample mean is defined as:
X = Xi
Previous work has studied the pro