Frequency Distribution; a table used to organize data. The left column include all possible responses on a variable being studied. The right Colum is a list of the frequencies or number of observations
for each class. Rule 1: determine k which is the numb
ECO 230
Economic Statistics
Azar Abizada
Fall 2011
Homework #3
Due date: Tuesday, September 27
Exercise 1: An insurance company estimated that 30% of all automobile accidents were partly
caused by weather conditions and 20% of all automobile accidents inv
Review class for the exam.
Sorry it is kind of late!
For number 6 in the midterm you are going to use the probability of the joint probability of
distribution. When they ask for the probability of x equal or less than 3 it is the sum of all the
probabilit
ECO 230
Economic Statistics
Azar Abizada
Fall 2011
Homework #1 (Solutions)
Exercise 1 (Excel).
a)
b)
c)
Exercise 2 (Weighted mean).
The firms cost of capital, a concept from corporate finance, is computed as a weighted average.
The idea is that a firm has
ECO 230
Economic Statistics
Azar Abizada
Fall 2011
Homework #2 (Solutions)
Exercise 1: A corporation takes delivery of some new machinery that must be installed and
checked before it becomes available to use. The corporation is sure that it will take no m
YOU HAVE TWO CASES WHEN THERE ARE TWO POPULATIONS
They are dependent and independent
When they here dependent you had to find the difference value and then the difference
average. Then you conducted the dbar test over the stdev of this
When it was indepen
ECO 230
December 6,2011
Review of the processes of Hypothesis testing again
Formulation of the Hypothesis
Example: new student registration system. At least 60% of the students favor the new system.
Hypothesis
Ho: p 0.6 (at most 60% of the students prefer
ECO 230
November 8/2011
1. Population of and has a sample of xbar and s
with xbar unbiased extimator of E(xbar)= most efficient with minimum variance
X depends on the confidence level
know use normal z and
unknown but n> 30 use z with s
unknown but n
ECO 230
1. Exam practice answers will not be provided
2. Chapters 5,6,7,8
3. 1 page of formula sheet
4. Proof questions might be included
5. 7.6 and 8.5 is not required
6. Exponential function
7. Exponential
a. Landa is the poison which is the number of o
Eco 230 November 17/11
Var(x+y)= varx+vary+2cov(x,y)
Var(x-y)=varx+vary-2cov(x,y)
Cov>0
Cov<0
Cov=0
Hypothesis testing
It is the rational framework for applying statistical tests.
The main question is whether the sample data is significant or not.
There a
Qusetion 9.40
H0: u< or = to 3
H1: u>3
Alpha is 0.05
If xbar is> u+z times sigma/ sqrt n then reject H0
3.07-3/0.4/sqrt 64
The z value is 1.4
Since 1.4 is less than 1.645 do not reject
Probability of rejecting H0 if the true mean is u= 3.1
You reject H0 i
Continuous Random Variable
A random variable is continuous if it can assume all possible values in the possible range
of the random variable.
A random variable can be measuring the time taken for something to be done. This is
continuous because there are
The exponential distribution is
Landa is the average number of some event occurring in a given period of time
F(x) =1- when x is greater than 0
If landa= 10 people per hour
What is the average time for the next successful event?
1/10 of an hour equals 6 m
ECO 230
Economic Statistics
Azar Abizada
Fall 2011
Homework #2
Due date: Tuesday, September 20
Exercise 1: A corporation takes delivery of some new machinery that must be installed and
checked before it becomes available to use. The corporation is sure th
Interquartile range: the spread in the idle 50% of the data. The difference between the observation at the 3 rd quartile and the 1st quartile. IQR=Q3-Q1 Variance: Chevychevs: For any population with
mean and standard deviation and k1. The percent of obser
Exercise 3: Let the random variable X follow a normal distribution with mean = 0.2 and 2 = 0.0025.
a)
b)
Find P(X) is > 0.4. P(X>0.4) = P(X-0.2)/0.05 >(0.4-0.2)/0.05) = P(Z>4) 0
c)
The P is 0.2 that X is > what number? We would like to find a such that P(
Estimators
November 1st
An estimator for a parameter is a function of the random variables and therefore it is itself a
random variable.
thus: the estimator is unbiased.
Unbiased In general we say that a sampling statistic in unbiased if its sampling
dist
1
2
3
4
5
6
A
40
30
40
34
28
35
B
42
35
45
41
24
41
D
-2
-5
-5
-7
-8
-6
Dependent ua-ub
Apply for some population
Dbar= sumation of d/n
Recall
A confidence interval is an interval calculated from a sample such that it will contain the true value
of a popu
Eco 230 Tuesday 25 October
F(x) = 1/10 -3<x<7
F(x)= x/10
X+3/10
Exponential
Landa is the poison which is the number of occurences
1/landa is the average number of the time
For # 7 use the formula 10s-7p -250
Cov(s,p) I found through correlation of s and p
Eco 230
Thursday October 27, 2011
Sampling distribution of Sample Variance
X1 X2 X3, XN
N(u, standard deviation) RS/n= (n-1)S^2/ variance to X^2 With degrees of freedom n-q
Any expected value of x^2 with degrees of K has expected value equal to k
Any vari
Eco 230
Population= complete set of all items that interest an investigator denoted by the letter N
Sample= observed subset of population values
Simple Random Sampling= a procedure used to select a sample from a population such that
each member of the pop
Eco 230
Information about the class
Office Hours: Monday from 12 to 1 pm and Wednesday from 1 to 2 pm
Recitations: Monday from 10 to 11 am and Friday from 12 to 2 pm.
Notes
Frequency Distribution
Frequency
Male
40
Female
30
Economics
Finance
Engineer
50
1
Eco 230
Range= difference between the maximum and the minimum
Quartiles
1
3
5
7
10
11
17
20
21
From 5 to 1 it is 25%
From 11 to 1 is 50%
From 20 to 1 is 75%
This is given by
Q1= .25 x (n+1)
Q2= .5 x (n+1)
Q3= .75 x (n+1)
Example
3
5
7
10
11
17
20
Q1= .25
Eco 230 Probability
In a situation you have several possible events. The probability of each event is a number
between 0 and 1. All the probabilities should add up to 1. Probability models are used to
study the variation in observes data so that inference
Eco 230
Example
Flip a coin
Sample is H or T
Role a die
Sample is 1,2,3,4,5, or 6
Flip a coin twice
Sample is HH TH HT TT
Example Flip a coin twice
Possible events:
Getting heads twice
Getting at least one head
Getting no heads
Getting at least one tail
E
Notes from Eco 230
A1
A2
A3
AK
This is mutually exclusive and collectively exhaustive.
P(B)=P(BA1)+ P(BA2)+P(BA3)+ P(BA4)+P(BA5)
Product Quality
A
B
Good
0.27
0.3
Bad=D
0.02
0.05
C
0.33
0.03
P(G)= P(GA)+ P(GB)+P(GC)
=0.90
P(Bad)= P(DA)+ P(DB)+P(DC)
What i
Rand
om
Varia
ble
S
A Random Variable gives a real number
Exam
ple:
Flip a
Coin
S:
X:
P(X=
0)
P(X=
1)
P(X=
2)
HH
Num
ber of
heads
HT
TH
TT
0
1
2
0,25
0,5
0,25
Example: Roll a die twice
S:
X:
1,1
Sum
of the
two
roles
1,2
1,3
6,5
6,6
2
3
4
12
Discrete RV: f