CHAPTER 5
STATISTICAL INFERENCE:
INTERVAL ESTIMATION
1. Statistical Inferencean Introduction.
2. Statistical Estimation
2.1.
Point Estimation
2.2.
Interval Estimation
3. Confidence Interval For the Population Mean
3.1.
Interval Estimate of
3.2.
The Margi
SYLLABUS
Z201: History of Rock and Roll Music
Section 23000 SPRING 2017
Instructor: RANDY ALBRIGHT
Contact me on CANVAS e-mail
Welcome.
This class has THREE exams, each worth 60 points, 180 total. In addition, you
will write TWO short essays, each worth 1
Name:
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The expression
P(1.96 /x+1.96 /)=0.95
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means:
Ninety five percent (95%) of the means from samples of size n deviate from the
population mean by no more than 1.9
CONFIDENCE INTERVALS
A confidence interval is an interval estimate for an unknown population parameter, which is built around a sample
statistic from a random sample, using MOE .
CI for
Sample statistic:
x
Confidence interval:
CI for
Sample statistic:
p
NAME:
You
Don't forget your name!
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Given are five observations for two variables, x and y.
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13. Monopoly
Jaesoo Kim
E201
Monopoly (E201)
1 / 45
Look for the answers to
Why do monopolies arise?
Why is P > MR for a monopolist?
How do monopolies choose their P and Q?
How do monopolies aect societys well-being?
What is price discrimination?
Monopoly
14. Oligopoly and Game Theory
Jaesoo Kim
E201
Oligopoly (E201)
1 / 47
(1) Basic concepts
In a strategic setting, a person may not always have an obvious choice
of what is best. A players optimal decision depends on the actions
of another person.
Game
A ga
E201. Quiz #11 (Mar 27. 2017)
Jaesoo Kim, IUPUI
1.
One would expect to observe diminishing marginal product of labor when
a. crowded office space reduces the productivity of new workers.
b. workers are discouraged about the lack of help from other workers
SAMPLING DISTRIBUTIONS
The Sample Mean is a Random Variable
The sample mean xx is a random variable. Its value is determined through a random sampling
process. The probability distribution of xx is called the sampling distribution.
How is the Sampling Dis
Example 1
Gallop reported in 2012 that 53% of American investors are likely to say the price of energy is hurting the
U.S. investment climate a lot. The survey results are based on questions asked in February 2012 of a
random sample of 1022 U.S. adults ha
What is a "Random Variable"?
A random variable is a variable quantity whose values are determined through a random experiment
or process.
Example of a random experiment:
Tossing a coin. The outcomes are heads or tails.
How does a random experiment generat
Hypothesis Testing
Next to interval estimates, test of hypothesis is the other leg of statistical inference. With hypothesis
testing we start with a hypothesis or a claim about the population parameter and use the sample data
to test for the validity of t
Selected exercises from Anderson Sweeney Williams, Statistics for Business and Economics (11th edition)
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Compute the mean, variance, and standard deviation of the following SAMPLE data:
x
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Car rental rates per day for a sample of
The solutions for the problems below are shown in the worksheet tab "SOLUTIONS" in this file.
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Consider the sample of size 5 with data values:
The mean of the sample is _:
x
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Hypothesis Testing
Next to interval estimates, test of hypothesis is the other leg of statistical inference. With hypothesis
testing we start with a hypothesis or a claim about the population parameter and use the sample
data to test for the validity of t
Key
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This is the solutions file. The solutions are below.
To see your score, enter your letter answers
Name: JOHNATHAN NGUYEN
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HW4
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Questions 1-4 are based on the following "POPULATION" data (N = 81):
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NAME:
Don't forget your name
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Important hint about computing p-value for a test statistic with a t-distribution:
When n > 30, you can approximate the tail area under the t-curve by
using the
LINEAR PROBABILITY MODEL CHECK OF RANDOM ASSIGNMENT
Another way to check for random assignment is to regress SMALL (an indicator, or binary variable)
on other characteristics and check for any significant coefficients, or an overall significant
relationsh
APPLICATION OF DIFFERENCE ESTIMATION: PROJECT STAR
In certain statistical analyses the features of one group are compared to the features of another. The
two groups are the treatment group versus the control group.
By randomly assigning subjects to treatm
THE DIFFERENCE-IN-DIFFERENCES ESTIMATOR
(HGG 7.5.5)
The DIDE is applied when we are interested in the changes in the explained variable by comparing
the "before" and "after" characteristics of data after an event, a policy change, intervenes.
In a situati
INTERACTION BETWEEN QUALITATIVE FACTORS
Intercept dummy variables for qualitative factors are additive: the effect of each qualitative factor is
added to the regression intercept. These qualitative factors are assumed independent. However, in
some cases,
Dummy Variables
Dummy variables allow us to construct models in which some or all regression model parameters,
including the intercept, change for some observations in the sample.
Example:
The hedonic model of predicting the value of a house
VARIABLES
Dep
THE LINEAR PROBABILITY MODEL
A linear probability model involves a binary dependent variable. What happens if we want to use
multiple regression to explain a qualitative event?
A binary dependent variable takes on only two values: zero and one.
A shopper
Random Variable
A random variable is a variable whose values are randomly assigned.
Example
Let x denote monthly sales of a commodity. Monthly sales is a random variable. The probabilities
are shown in the f(x) column.
x
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NORMAL DISTRIBUTION
The normal distribution is the distribution of continuous random variable. Generally, the function
describing the distribution of a random variable is called a probability density function (PDF). The
PDF of a normally distributed rando
QALITATIVE FACTORS WITH SEVERAL CATEGORIES (Text 7.2.2)
Many qualitative factors have more than two categories. For example, in the WAGE equation, in
addition to RACE and GENDER, we can include geographic regions (North, South, East, West); level of
educa
BASIS STATISTICAL CONCEPTS
Sum of .
Mean
x =
y =
29730
2441
xx = x/n
n=
20
xx =
1486.5
yx =
122.05
1486.5
122.05
x=
y=
1900
135
x xx =
y yx =
Sum of deviations
(x xx ) =
(y yx ) =
0
0
Squared deviation
x=
y=
Deviation from the mean
Sum of quared deviation
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The expression
P(1.96 /x+1.96 /)=0.95
a
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means:
Ninety five percent (95%) of the means from samples of size n deviate from the
popul