The Normal Distribution
Statistics and Data Analysis Summer 2015
1
The Normal Distribution
Very important distribution in statistical theory
Many phenomena around us and in nature are
modeled by a normal distribution
Quality characteristics of finished

Complementary Events / Counting Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
Probability
1. When rolling a die, event the outcome is even. What is the probability of the event ?
Solution: There are 6 elementary outcomes, al

Discrete Random Variables Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
Discrete random variables: PDF & Expectation
1. Consider the following game:
1. You pay $6 to flip a coin.
2. If the coin lands heads, you get $10; othe

Statistics for Business Control and
Regression Models
STAT-UB.0103.003
Instructor: Xi Chen
1
Course Information
Instructor: Xi Chen ([email protected] )
Office: KMC 8-50
Office Hours: Mon, Thu: 11:00 AM to 12:00 AM
Teaching Fellow: Yilin Zhou ([email protected]

Chapter: 3
Probability
What you will learn
1.
2.
3.
4.
Events, Sample Spaces, and Probability
Unions and Intersections
Complementary Events
The Additive Rule and Mutually
Exclusive Events
5. Conditional Probability
6. The Multiplicative Rule and
Independe

Confidence Intervals Solutions
STAT-UB.001 Statistics for Business Control
Confidence Interval
1. A random sample of 36 measurements was selected from a population with unknown mean
and known standard deviation = 18. The sample mean is x
= 12. Calculate

Statistics for Business Control &
Regression/Forecasting Models
Chapter 1
Statistics, Data, &
Statistical Thinking
1
What you will learn
1. Introduce the field of statistics
2. Demonstrate how statistics applies to business
3. Establish the link between s

The Central Limit Theorem Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
The Central Limit Theorem
1. You draw a random sample of size n = 16 from a population with mean = 100 and standard
deviation = 20. From this, you compu

Inferences Based on Two Samples Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
Comparing Two Populations
1. Here are boxplots of the passing distances (in meters) for a bike rider with and without a
helmet. Is there evidence

Multiple Regression, F Tests Solutions
STAT-UB.0103 Regression and Forecasting
Multiple Regression
1. We have a dataset measuring the price ($), size (ft2 ), number of bedrooms, and age (years) of
518 houses in Easton, Pennsylvania. We fit a regression mo

Hypothesis Tests Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
Null and alternative hypotheses
1. General Mills claims that there are 16 ounces of cereal in the average box that they manufacture.
As a consumer advocate, you

Introduction to Linear Regression Solutions
STAT-UB.0103 Statistics for Business Control and Regression Models
Linear Regression
1. Consider two variables measured on 294 restaurants in the 2003 Zagat guide:
y = typical dinner price, including one drink a

Review of Final Exam
Chapter 11
Simple Linear Regression
1
Introduction
Usually one of the variables is naturally
seen as causing, influencing, or
predicting the other variable
X variable
independent variable, predictor, explanatory
variable
Y variabl

Avijit Singh (as10347)
Homework #1, Sept 15 2016
Problem 7:
A)
B)
The airline, which has an unusual mix of part time and full time employees, is Federal Express.
Avijit Singh (as10347)
Problem 8:
1)
2)
Homework #1, Sept 15 2016
Avijit Singh (as10347)
Home

Chapter 8
Inferences Based on Two
Samples: Confidence Intervals
and Tests of Hypothesis
Content
1. Target Parameter: difference between two
population means
2. Comparing Two Population Means:
Independent Sampling
3. Comparing Two Population Means: Paired

Normal CDF: use (z) table
z=
x
Normal Random Variable: use (z) table
Ex. Suppose z is a standard normal random variable. What is P(z1.2)? .
8849
Central Limit Theorem: Averages behave like normal random variable
Ex. If x1, x2, , xn are independent sample

Project Assignment I (Hmw #10)
and Solutions. Review Questions 4, 5, 6, 7, 8, and 10.
Project Assignment II and Solutions. Review Questions 5 through 12. (Be sure you
download the latest version of the Solutions.)
Project Assignment III. Based on Question

Hypothesis Testing
Statistics and Data Analysis Summer 2015
1
Hypothesis Testing
Do investment experts pick stocks better than
dart-throwing amateurs? WSJ tested as follows
Four experts pick a stock each
Four stocks are chosen by randomly throwing darts

Random Variables and
Probability Distributions
Statistics and Data Analysis Summer 2015
1
Random Variables
Question: A coin is tossed three times; what is
the probability you will get two heads?
A random variable (RV) is something that takes
on numerica

Simple Linear Regression
Statistics and Data Analysis Summer 2015
1
Introduction
Often want to study the relationship between two
variables
SAT score and first-year GPA at a university
Advertising budget and sales
Leg space and satisfaction from flight
D

Multiple Regression
Statistics and Data Analysis Summer 2015
1
Introduction
Often there are several factors that influence a
Y variable
Example 1: salary (y) may depend on
experience (x1), education (x2), and gender (x3)
Understanding the relation betwe

HW 2
1) Consider the data on performance of mutual funds, Eg 3 from Handout 3. Past
Loser indicates that the fund lost value over some period in the past (as specified in
Goetzmann and Ibbotsons study.) Current Loser indicates that the fund lost value
in

Sampling, Point Estimation
and Interval Estimation
Statistics and Data Analysis Summer 2015
1
Sampling
Q: What is the average income of all Stern
students?
Finding the exact answer (examining everybody)
is difficult
Solution: examine a sample of studen

STAT-UB.0103
Prof. Tatum
Midterm 2 Study Guide
11-20-15
1. Review the following homework assignments and Solutions, as well as your related
class notes and text sections.
Homework 6: Poisson and Normal distributions
(Chap. 4.5 and 4.6)
Homework 7: Samplin

STAT-UB.0103, 12-16-15
Prof. Tatum
Final Exam Study Guide
The Final will cover regression, starting at Homework 9 through the end of the semester.
Working on your project is excellent preparation for the Final because the questions will
likely be similar.

STAT-UB.0103, 12-5-15
Hmw10 Solutions
Project Assignment Part I
Prof. Tatum
1. Show the first ten rows of your stock returns and of S&P%, with the dates.
2. Using Excel, regress your stock returns and of S&P%. (Be careful to get y in the right
place.)
3.

STAT-UB.0103
Prof. Tatum
Homework #6 Solutions, Section 2
NORMAL DISTRIBUTION
Suppose the monthly percentage change for the S&P500 follows a Normal
distribution with =0.79% and =1.3%.
(a) Sketch the distribution by hand. Be sure to show and the 2 points o

STAT-UB.0103, 11-16-15
Prof. Tatum
Homework #9 Solutions
Note the
correction to the subscript
s
in the equation for (e): s1
SSxx
1. Answer the following questions using the Net Weight (y) and Count (x) data for the six
bags of Peanut M&Ms shown below.
x