NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
Statistics ECON-UB.18.011: Fall 2011
Professor Roman Frydman
Solutions to TEST#1
Please answer all questions.
Total 25 points.
Problem 1 .
(4 points)
Consider the following sample cfw_1, 2, 3, 4, 5.
A) What numb
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics, Fall 2011
HOMEWORK 3
DUE FRIDAY OCTOBER 7 2011.
PLEASE HAND IN THE CLASSROOM AT THE BEGINNING
OF CLASS
Problem 1
Consider an experiment involving three tosses of a fair coin. Dene a
r
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics, Fall 2011
HOMEWORK 6
DUE MONDAY NOVEMBER 21 2011 BEFORE 5PM
in your TAs mailbox on the 6th oor, 19 West 4th Street .
Problem 1 An insurance company is considering settling small claim
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
Statistics ECON-UB.18.011: Fall 2011
Professor Roman Frydman
TEST#2 (2 hours)
Please answer all questions.
Total 25 points.
(3 points)
Problem 1
As the price of gasoline continues to rise, many drivers are avoid
Problem Set 1
Due: Monday Sep 19th before 5pm Yu-Wei Hsiehs mailbox
6th oor, 19 W. 4th Street
Problem 1 2.2/38
Problem 2 2.20/48
Problem 3 2.42/61 and applet exercise 2.1
Problem 4 Applet exercise 2.6/69
Problem 5 2.80/75
1
Problem Set 2
Problem 1 Create 100 observations of a Normal Random Variable with
mean = 0 and standard deviation = 1.
a Create the histogram. What can you tell about the histogram?
b Calculate descriptive statistics
c Are the mean and the median close to
Solutions to HW4
Problem 1
(1) Yes. With n=20 and p=0.3
(2) P (Y = 5) = P (Y <= 5) P (Y <= 4) = 0.416 0.238 = 0.178
(3) P (Y <= 5) = 0.416
(4) Compute P (Y = Yi ) for all possible Yi (that is, all integers from 0
to 20)
.
P (Y = 5) = 0.178
P (Y = 6) = P (
Problem 1.
The purpose of this exercise is to understand the sampling distribution of sample
mean. We will create 100 samples (100 rows). In each sample (row), we will simulate
25 random outcomes (25 columns), and store the sample mean for each row in C26
Solution of Problem Set 2
Problem 1
a&b. Calc>random data>normal
Number of rows of data to generate: 100
Store in column: C1
Mean: 0
Standard Deviation: 1
Then go to Stat>Basic Statistics> Graphical Summary
Summary for C1
A nderson-Darling N ormality Test
Solutions to the Review Problems
Problem 1
Let cfw_Xi N be the list of original numbers. We know that X
i=1
)2 = 10
X
(a) Let Yi = Xi + 20
1
N
1
N
N
=
1
N 1
N
i (Xi
Yi
i
(Xi + 20)
i
Xi +
i
=
s2
y
Xi = 50 and s2
x
N
1
N
N
i
N
=
Y
1
N
1
N 1
N
1
N 1
20
i
Problem 1.
The purpose of this exercise is to understand the sampling distribution of sample
mean. We will create 100 samples (100 rows). In each sample (row), we will simulate
25 random outcomes (25 columns), and store the sample mean for each row in C26
Statistics Problem Set 2
September 26, 2011
Problem 1
a.
This histogram is great for figuring out the distribution of the data which is concentrated
mostly between 0 and 1. You cannot see individual data in this graph. The data
distribution is not exact s
Solutions to the Review Problems
Problem 1
Let cfw_Xi N be the list of original numbers. We know that X
i=1
)2 = 10
X
(a) Let Yi = Xi + 20
1
N
1
N
N
=
1
N 1
N
i (Xi
Yi
i
(Xi + 20)
i
Xi +
i
=
s2
y
Xi = 50 and s2
x
N
1
N
N
i
N
=
Y
1
N
1
N 1
N
1
N 1
20
i
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics
M 9:30 10:45; F 9:30-12:15 SILV 401
Fall 2011
Professor Roman Frydman
[email protected]
19 West 4th Street, Room 515
Office hours: Friday 12:15-1:15 and by appointment.
Teaching As
Brian Cabrera
September 19th, 2011
Yu-Wei Hsieh
Problem Set 1
Problem 1
a. Frequency:
X8
Y9
Z3
b. Relative Frequency:
X 8/20= 40%
Y 9/20= 45%
Z 3/20 = 15%
C.
D.
2. a. Class None-0 contains the highest proportion of respondents.
b. .06
c. .06
d. .88
Guide to Minitab
Prof. Roman Frydman
TA:
Yu-Wei Hsieh
Taisuke Nakata
1. Import Data
There are several ways to load data into Minitab.
a. key-in data in the worksheet
C1, C2is the variable name. Labels can be added in the second row.
You can also enter dat
Getting Started with Minitab
Prof. Frydman
September 4th, 2003
1
Handling the le
To open the data le,
go to File>Open Worksheet
Then select the le with the extension .dat and
then click option and choose Free Format then OK then Open
To save the le(w
Brian Cabrera
October 31, 2011
Homework 5
Problem 1
YES; the mean is between 1.9771 and 2.0199 and my expected mean was 2. This is simply
because an average of 3 and 1 is 2.
Problem 2
Summa r y f or C2 6
A ndersonD arling N orm alit y T est
A Squared
PV a
Brian Cabrera
Statistics, Fall 2011
Homework 4
1)
a.
b.
c.
d.
e.
Yes, it is a measure of 2 possible outcomes (x) a (n) number of trials.
0.17886305056988
0.41637082944781
X at least 5; at a probability of 0.762492221122399
Expected value among next 20 cus
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics, Fall 2011
HOMEWORK 4
DUE MONDAY OCTOBER 24 2011 BEFORE 5PM
in your TAs mailbox on the 6th oor, 19 West 4th Street .
Problem 1 A chain of motels has adopted a policy of giving a 3% dis
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics, Fall 2011
HOMEWORK 5
DUE MONDAY OCTOBER 31 2011 BEFORE 5PM
in your TAs mailbox on the 6th oor, 19 West 4th Street .
Problem 1 Create 500 samples of size 25 from a uniform distribution
NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON-UB.18.011: Statistics, Fall 2011
REVIEW PROBLEMS: SET 1
Problem 1
The mean and standard deviation of a list of numbers are 50 and 10,
respectively.
Suppose that the number 20 is added to each number. What a