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
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
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
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
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 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
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
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
Econ 3640-001
Probability and Statistical Inference
Lecture Notes on 09/17/13
Measures of Spread
Measures of Relative Standing
Normal Distribution
Example
Suppose there are two stocks: stock 1 and stock 2. Below are the
historical prices of stock 1 and st
Econ 3640-001
Probability and Statistical Inference
Lecture Notes on 09/24/13
Normal Distribution
Tips on Using Table
To calculate the area between two z-values, first get the area under
N(0,1) to the left for each z-value from Table A.
Then subtract the
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
Practice Problems 2 Solution
Q1. Suppose there are 40 students in a class taking the midterm. The highest mark in this exam was
90 out of 100, and the lowest mark was 60 out of 100.
1) Please try to find the possible maximal and minimal standard deviation
1.
ASSIGNMENT 2
Write a sample space of outcomes from rolling a dice once and draw a histogram of probability
distribution
SAMPLE SPACE
SCORE
1
SCORE
5
SCORE
2
SCORE
6
SCORE
3
SCORE
4
6 SIDED
DICE ROLL
ASSIGNMENT 2
Is the probability normally distributed?
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: sophiewu.pro@gmai
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
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
Econ 3640-002 Quiz 4_Chs 7 & 8
Uid:_; Name_
Use the following to answer questions 12:
An SRS of 100 postal employees found that the average time these employees had worked for the
postal service was x = 7 years, with standard deviation s = 2 years. Assume
Econ 3640-002 Quiz 3_Chs 5 & 6
Uid:_; Name_
Use the following to answer questions 1-2:
In the game of roulette, a metal ball is spun around a rotating wheel containing 18 red-numbered
slots, 18 black-numbered slots, and 2 green slots numbered 0 and 00, re
CHAPTER 8 REVIEW QUIZ (11 POINTS)
Use the following to answer questions 1-2:
A researcher is studying the failure rate of restaurants. She selects a random sample of 200 restaurants in large
cities that opened within the last year. Following up on these r
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
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(
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 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
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
CHAPTER 3
1.
Can pleasant aromas help a student learn better? Two researchers believed that the
presence of a floral scent could improve a persons learning ability in certain situations.
They had 22 people work through a pencil-and-paper maze six times: t
CHAPTER 1
Use the following to answer questions 1-2:
In a Business Statistics class with 136 students, the professor records how much money each
student has in their possession during the first class of the semester. The histogram below is of
the data col
CHAPTER 4
Use the following to answer questions 12:
You select an employee at random from all those in a large company. An employee can be
either male or female, and can be under 30 years old, between 30 and 45 years old, or over 45
years old. The table b
CHAPTER 2
1.
Consider the following scatterplot.
50
Y
40
30
20
15
X
20
25
The correlation between X and Y is approximately:
A) 0.999.
B) 0.7.
C) 0.0.
D) 0.7.
Ans: B
2.
Which of the following is true of the correlation coefficient r?
A) It is a resistant m
CHAPTER 6
1. Nine airlines are selected at random. For each airline, we record the current fee for
checking a single bag. The average for these 9 airlines is x = $25. Assume that the
current fee follows a normal distribution with unknown mean and standard