Q21 (14.50) Franchise headquarters claims it randomly selected the
local franchises that received surprise visits during the past year. The
sequence of visits is as shown below for male (M) versus female (F)
mangers. Using the 0.10 level of significance,
PROBABILITY
Probability is the measure of ones belief in
the occurrence of a future event.
Circumstances
Event
Probability
Flip a coin
Heads.5
Roll a die # > 4 .33
Roll 2 dice
Sum = 7
.167
2016 MLB Playoffs Yankees win WS ?
Set Theory
We will use capit
ESTIMATION
The purpose of statistics is to use
information contained in a sample to make
inferences about the population from which
the sample was taken.
Because populations are characterized by
numerical descriptive measures called
parameters, the objec
Properties of Point Estimators
Definition 9.1 Given two unbiased estimators 1
and 2 of a parameter , with variances V(1) and
V(2) respectively then the efficiency of 1 relative
to 2 denoted eff(1 , 2) is defined by the ratio
eff(1 , 2) = V(1)/V(2)
Defini
Functions of Random Variables
Consider the problem of estimating the
population mean using a random sample
of n observations y1, y2, yn
As our estimate of we would use
= ( yi )/n
What is the error of estimation (ie the difference
between the estimate a
Sampling Distributions
Throughout this chapter. We will be
working with functions of the variables Y1,
Y2, Yn observed in a random sample
selected from a population of interest.
For example if we want to estimate a population
mean , we obtain a random sa
Sampling Distributions
Throughout this chapter. We will be
working with functions of the variables Y1,
Y2, Yn observed in a random sample
selected from a population of interest.
For example if we want to estimate a population
mean , we obtain a random sa
Stat Decision Making
1.
Class 20: Model Building
R.J. Brent
Introduction.
Here we extend the regression model to situations where the underlying
relation is not linear. There are two basic approaches:
A non-linear (polynomial) model may be applied to the
Stat Decision Making Class 22:Time Series and Forecasting 1 R.J. Brent
1.
Introduction
(i)
Extension of the regression model:
Time series data: Data consists of observations that are a sequence
over regular time intervals.
So instead of a sample xj wher
Stat Decision Making Class 14: Simple Linear Regression 1 R.J. Brent
1.
Introduction.
In the previous part of the course, hypothesis testing, we looked at
two (or more) means to see if the difference was significant or not.
In this chapter we look at al
Stat Decision Making Class 11: Nonparametric Methods 1
R.J. Brent
1.
Introduction.
(i)
Nonparametric tests, like parametric tests, are based on the
principles of hypothesis testing.
(ii)
These tests do not assume that the population from which the
sample
Stat Decision Making
1.
Class 17: Multiple Regression 1
R.J. Brent
Introduction.
This is an extension of the linear regression model to more than
one (multiple) independent variable. This is called multiple
regression.
The relationship between the depen
Stat Decision Making
Class 8: Chi-Square Applications
R.J. Brent
In Chapter 11, and for much of Stats 1, we assumed that the population
distributions were normally distributed.
Now we show how we can test this or other distributional assumptions
(e.g., in
Stat Decision Making
Class 4: Analysis of Variance (ANOVA)
R.J. Brent
Chapter 11 showed how to compare two means to see if the difference is
statistically significant.
Now extend this comparison to the case where there is more than two sample
means.
1.
Ke
Stat Decision Making
1.
Class 1: Review of Stats 1
R.J. Brent
Sampling. (Ch. 8)
Population distributions and sample distributions.
(a) The population distribution is the complete set of possible
outcomes for x, a random variable.
The mean of this distribu
Discrete Random Variables and
their Probability Distributions
Definition 1. A random variable is a real
valued function for which the domain is a
sample space. Random variables are
denoted by capital letter such as: X,Y or Z
Examples: For population of
STATISTICS
Statistics is the science of determining the
distribution of a characteristic within a
population.
Examples
1. GMAT Scores among Fordham GBA
students
2. Household income within Bergen Co.
3. Age among the NY Yankees players
Why is this im
Multivariate Probability
Distributions
We often are interested in the intersection
of 2 or more events for example the height
and weight of a selected individual
DEFINITION 5.1 Let Y1 and Y2 be discrete r.v. The
joint probability function for Y1 and Y2 i
Notes
Central tendency
Mean (arithmetic average)
Population Mean M=sum/population size
Sample Mean M=sum/# of observations in the sample
Median (Middle Value)
Find the center of the data, if there is no center then average the middle two
numbers
Weighted