CHAPTER TEN
Statistical Inferences about Two Populations
D
M
BApp
1.
Restaurateur Denny Valentine is evaluating two sites, Raymondville and
Rosenberg, for his next restaurant. Prevailing images of the two suburbs imply
that Raymondville residents (populat
EC255
Lecture #6
September 29 th, 2016
Variance and Standard Deviation of a Discrete Distribution
E X
N
i1
x i P x i 0 . 8
2= 3.960
= 1.990
Binomial Distribution
Experiment involves n identical trials
Each trial has exactly two possible outcomes: success
BU255: Statistics Exam-AID
By: Greg Overholt
Some images used from course slides
Agenda
THANK YOU
Chapter 1-7
1
THINGS I KNOW.
Chapter 1
What is statistics?:
A a way of getting information from data
It is a pattern language
Is the science of estimat
BU255 FINAL Exam-AID
Taught by: Greg Overholt
What are we doing?
Stats
Lectures 10 to 20!
All of it.
Lecture 10 & 11:Estimation
Chapters 5 and 6:
Binomial, Poisson, normal, and exponential
distributions allow us to make probability
statements about X
EC255
Chapter 1 Intro to stats
13th September 2016
Types of Data:
Data
Type of Data
Quantitative
Qualitative
Types of analysis
Nominal
Level
Most basic type
Ex. Eye Color,
martial status,
SIN #, ID#
Cant do more analysis
You can just count
Ordinal
Discre
EC255
Chapter 3 Descriptive Stats
15th September 2016
There are three common measure of central tendency that provide info about
location
Mode
Median
Mean
Mode: value that has the highest frequency
Not affected by extreme value
There may be no mode
EC255
Chapter 4
20th & 22nd September 2016
Chapter 4: Probability
Set of all possible events for experiment is denotes by S also called
sample space.
Experiment: A process that produces an outcome
More than one possible outcome
Only one outcome per tr
EC255
Chapter 2
15th September 2016
ONLY COVERED SECTION 2.1 & 2.2 OF THE TEXTBOOK
Ungrouped data (Raw data) vs. grouped data
Ungrouped data is not aggregated on the other hand grouped data is
summarized which makes it easier to understand and interpret
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Types of data
time series data (Yt for t=1,T)
cross-sectional data (Yi for i=1,N)
panel data (Yit for i=1,.,N and t=1,T)
Data Sources
Library
Government statistical offices (CANSIM)
World Wide Web
quote.yahoo.com (financial data)
UBC Pacific Data Service
October 18th, 2016
EC255
Chapter 7a: Sampling & Sampling Distributions
Reasons for Taking a Census
Eliminate the possibility that by chance a random sample may not be representative of
the population
For the safety of the consumer
Reasons for Sampling
EC255
Lecture 2
Population: Collection of all possible elements of interest
Ex. If one wants to find average age of students and ALL students are talked to, this is the
general population
Census: Study all subjects in the population (collection of the val
EC255
Lecture 3
The notation is important because it can differ for population and sample
Capital N is population
n is count in sample
Measures of Variability Ungrouped Data
Used to indicate how much the observations are spread out around the mean
Commo
Chapter 8: Statistical Inference: Estimation for Single Populations
135
Chapter 8
Statistical Inference: Estimation for Single Populations
LEARNING OBJECTIVES
The overall learning objective of Chapter 8 is to help you understand estimating parameters of s
Statistics Midterm #1 Review (Weeks 1-4)
Week 1
Chapter 1: Introduction
Vocabulary
Measurement: process of transforming something our senses cannot perceive into
something they can perceive.
Data: measurements that are collected, recorded, and summarize
EC255
Lecture 6
Oct.4 th/ 2016
Probability Distributions: A table, formula, or graph that describes that values that a random
variable can take and their respective probability
Discrete probability distributions: Binomial, Poisson
Continuous probability d
EC255
Lecture #5
September 27 th, 2016
Pop Question
A survey found that 43% of people will save money
On the other hand, 45% of people plan to reduce debt
Of those who expect to save money, 81% plan to reduce debt
M= save money
R= Reduce debt
1) What i
October 20th, 2016
EC255
Chapter 7b: Sampling & Sampling Distributions
Sample Distribution of x-bar
z
x
x
x
x
n
x
x
n
x-bar- Example 1
Suppose a population has mean of 8 and standard deviation of 3
Suppose a random sample of size n=36 is selected
What
EC255
Lecture 4
Sample Space: Set of all possible events for experiment, usually donated by S (outcome is not
known but we are known of probability)
Example: All sides of a dice (s) (1,2,3,4,5,6)
Example: Pick a card s=all 52 cards of a bridge deck
We can
EC255
Chapter 1 Intro to stats
Statistics: Art and science of gathering, analyzing, interpreting, and presenting data
Types of data:
Qualitative: Label or name for characteristics (metric data)
Quantitative: Measurement of amount or quality (non-metric da
Chapter 8a: Estimation for Single Populations
Last week
Key idea: No study is done yet
Only some information was present and how likely was it to get a sample mean
This week:
After the study has been done
Results are present
No new formulas
Using sa
Assumption 1
A1 is simply saying that on average, the value of the error term is zero.
Remember the error term captures the effect of missing variables, misspecified functional forms, shocks.
Incorporate prior information if we know exactly what we are mi
Ordinary Least squares
Given the basic model
Yi = + i + ui
X
i = 1, ., n
The OLS Estimation means minimizing the sum of square residuals by
choosing the alpha hat and Beta hat
The residual
hat
u hat is the estimated error term which is defined by Y - Y
We
EC255 Chapter 3 Textbook: Descriptive Statistics
3.1 Measures of Central Tendency: Ungrouped Data
-Measure of Central Tendency: Yield information about the centre, or middle part, of a group
of numbers
E.g. A table of Price-to-Earnings Ratio: Measures of
EC255 Chapter 2 Textbook: Charts and Graphs
2.1 Frequency Distributions
-Frequency Distributions: A summary of data presented in the form of class intervals and
frequencies
-Range: The difference between the largest and smallest numbers
When constructing
EC255 Chapter 4 Textbook: Probability
4.1 Introduction to Probability
-Much statistical analysis is inferential, and probability is the basis for inferential statistics
-Inferential statistics involves taking a sample from a population, computing a statis
EC255 Chapter 4: Bayes Rule
Conditional Probability
-Conditional probability for events E1 and E2:
-The ratio of the relative size of E1 E2 to E2 is P(E1|E2)
Bayes Rule
-An extension of Conditional Probability
-Used to review prior probabilities with new
EC255 Chapter 5: Discrete Distributions
Learning Objectives
-Distinguish between discrete random variables and continuous random variables
-Compute mean and variance of a discrete distribution
-Understand the binomial distribution and its applications
Dis
EC255 Chapter 3: Descriptive Statistics
Numerical Data Properties
-Central Tendency: Location
-Variation: Dispersion
-Shape
Measures of Central Tendency: UNGROUPED Data
-Provide information about the center or middle part of a
numbers
-Provide location in