Law of large numbers
As the number of randomly drawn
observations in a sample increases,
the mean of the sample
x gets
closer and closer to the population
mean m.
This is the law of large numbers. It
is valid for any population.
Note: We often intuitively
CHAPTER 8
1. A statistician working for the National Basketball Association supplies the television
announcers with interesting statistics. At a certain point in the season, he discovered that
of the 375 games where a team was winning the game at the end
Econ 3640-001
Lecture Note #8
Fall 2012, Hyeon Kim
Lecture Note #8 Inference for Proportions (Chapter 8)
1. Inference for a single proportion
Many studies collect data on categorical variables, such as race or occupation of a person, the
make of a car, et
Econ 3640-001
Final Exam
2013 Fall
Instruction:
1. This take-home exam is due on December 20th, 2013 at 10:00 am. You need
to submit your answer before this deadline. Late su
Econ 3640-001
Practice Questions (Final)
Fall 2016, Hyeon Kim
Practice Questions for the Final
1. The final exam will cover from chapter 6 to chapter 8 (but still need the concepts covered previous chapters)
2. It is the take-home format like the 2nd midt
Econ 3640: Quiz 1_Chs 1 & 2
Uid:_; Name_
Use the following to answer questions 1-2:
Each of the following two histograms represents the distribution of acceptance rates (percent
accepted) among 25 business schools in 2005. The histograms use different cla
Econ 3640: Quiz 2_Chs 3 & 4
Uid:_; Name_
1.
A television station is interested in predicting whether voters in its listening area are in
favor of federal funding for railroad improvements. It asks its viewers to phone in and
indicate whether they are in f
2
Student: _
1.
A frequency distribution for qualitative data groups these data into classes called intervals and records the
total number of observations in each class.
True False
2.
The relative frequency of a category is calculated by dividing the cate
Econ 3640-001
Practice Questions #1
Fall 2012, Hyeon Kim
Practice Questions for the 1st Midterm
1. The first midterm will cover from chapter 1 to chapter 3.
2. This practice questions will be the best material for the exam: All of exam questions will be s
Econ 3640-001
Practice Questions (Final)
Fall 2012, Hyeon Kim
Practice Questions for the Final
1. The final exam will cover from chapter 6 to chapter 8.
2. This practice questions will be the best material for the exam: All of exam questions will be simil
Practice Problems 4
SAMPLING DISTRIBUTION OF SAMPLE MEAN (textbook: Ch 4.4)
Q1. A normally distributed population has a mean of 40 and a standard deviation of 12.
(1) What does the central limit theorem say about the sampling distribution of the mean
if s
1 P( 0 < Z < 1.5)
0.4331927987
P(-1.5 < Z < 1.51)
0.8676710866
P( Z < 2.84)
0.9977443233
P( Z > 3.54)
0.0002000635
Z.045
1.6953977103
Z.20
0.8416212336
X is normally distributed with mean 100 and standard deviation 20. What is the probability that X is gr
Practice Problems 3
Updated on Oct 9th, 2013
* Using Excel, looking at the Table, or utilizing other software may generate slightly
different number in your answer. *
Q1. Cartridge Story
(a)
N ( , ) = N(11,500, 800)
P(X>12,000)= P(
( x) (1200011500)
)= P(
Practice Problems 3
Q1. Cartridge Story. The number of pages printed before replacing the cartridge in a
laser printer is normally distributed with a mean of 11,500 pages and a standard
deviation of 800 pages. A new cartridge has just been installed.
a) W
Econ 3640-002
Lecture Note #2
Summer 2014, Hyeon Kim
Lecture #2: Examining Relationships (Chapter 2)
Introduction
Most statistical studies involve more than one variable in which we are usually interested in the
relationships between those variables. Spec
Practice Problems 4
SAMPLING DISTRIBUTION OF SAMPLE MEAN (textbook: Ch 4.4)
Q1. A normally distributed population has a mean of 40 and a standard deviation of 12.
(1) What does the central limit theorem say
Lecture Notes
Hypothesis Testing
I. Given unknown, known (Normal Distribution)
Q1. In recent years, a number of companies have been formed that offer competition to AT&T in
long-distance calls. All advertise that their rates are lower than AT&T's and as a
Assignment 3
Continuous Probability Distributions
Instruction:
Assignment 3, as part of preparation for hypothesis testing questions in assignment 4, aims to help increase your
familiarity with Excel commands for different continuous probability distribut
Assignment 3 Solutions
* Please check your answers before you turn in. You need to turn in your Excel file. *
Due Dec 8th, Sunday, by 11:59 pm
1. Normal Distribution
(a) P( 0 < Z < 1.5)
=normsdist(1.5)-normsdist(0)
Answer
(b) P(-1.5 < Z < 1.51)
=normsdist
Provinces and Territories
Population
Total Area
Ontario
12,851,821
1076395
Quebec
7,903,001
1365128
British Columbia
4,479,934
925186
Alberta
3,645,257
642317
Manitoba
1,208,268
553556
Saskatchwan
1,033,381
591670
Nova Scotia
921,727
53338
New Brunswick
7
ASSIGNMENT 1
Econ 3640-001 Probability and Statistical Inference
FALL 2013
HOSTEL MARKETS SURVEY FOR NEW YORK CITY AND PARIS
Instructions:
1) Please submit two electronic copies of this assignment: one to your Canvas
account, the other to the instructors
ASSIGNMENT 2
Econ 3640-001
FALL 2013
Probability and Statistical Inference
Portfolio Diversification
Instructions:
1) Please submit two electronic copies of this assignment:
one to your Canvas account, the other to the instructors
email: [email protected]
Lecture Notes for Statistical Hypothesis
(using assignment 1 and assignment 4 example)
Objective:
1. Inference about a population mean when the standard deviation is unknown
(Example: Was our previous calculation for the average price per bed per night co
Assignment 4
Hypothesis Testing
Due: December 8th, 2013 by 11:59pm
Instruction
In Assignment 1, you were asked to record the price per night per bed from at least 15 hostels in
New York City and Paris, respectively. After you calculated the sample mean an
Practice Problems 5
Q1. Four candidates are running for mayor. The four candidates are Adams, Brown, Collins, and
Dalton.
(a) Determine the sample space of the results of the election.
(b) Employing the subjective approach, a political scientist has assig
Practice Problems 6
1. There are 80 multiple-choice questions in a single test. Each question has four possible answers,
and one of which is correct. Suppose a student who didn't study for the exam can only answer by
guessing. What is the probability that
Econ 3640-001
Probability and Statistical Inference
Lecture Notes on 08/29/13
Examining Distributions
Displaying Distribution with Graphs
iTunes Example
Credit Card Example
A credit card company studies the spending behavior of their 21- to 25year-old cus
Econ 3640-001
Probability and Statistical Inference
Lecture Notes on 09/12/13
Measures of Spread
Measures of Relative Standing
Normal Distribution
Stemplot
Purpose
Works well for small data sets quick and easy
Alternative display for quantitative data
Giv
Chapter Six
Sample distribution of sample mean
If x
is sample mean of an SRS of size n from population with mean and sd , then x = , and
x = n
When a random sample with size n is drawn from a N (, ), then the sample mean will follow N (, n )
Central l
Homework 2
Zhi Li
July 13, 2017
1. A survey on college students show that 40% of the students like country music, 30% like gospel music,
and 10% like both of them.
What is the conditional probability that a student likes gospel music if he or she likes c
Chapter Seven
T-distribution
Normally, we dont know the real value of population parameter, so we can only rely the informatin provided
by observations.
Standard error: When the standard deviation of a statistic is estimated from data, the result is calle
Assignment One
Zhi Li
June 30, 2017
Instructions:
1. You should upload a file containing the R code and the result in the Canvas for me to view
2. The format of the fies can be in pdf, word, or HTML
Question 1 (20 pts)
1. If X N (2, 1.5), calculate the pr
Homework 3
Zhi Li
July 20, 2017
1. You did a little random survey about sudents height (unit is in inches) in our school and the data
is stored in Height.rda data file. You know the standard deviation for population is 4 inches (This
information is very i