Statistics
Problem Set 6
Cichello: FA 13
Problem Set 6
Due: 5:00 pm, Saturday, November 2nd
The graded portion of this homework is found on MyStatLab . Answers to any questions
submitted after 5:00 pm on Saturday, November 2nd will be given half credit.
P
Statistics
Problem Set 6 SOLUTIONS
Cichello: FA 13
SOLUTIONS
Problem Set 6
Chs. 7.17.4 and 9.19.4: Estimation, Confidence Intervals and Hypothesis Testing
1)
a. Explain the difference between an estimate and an estimator.
An estimator is the recipe (or
Statistics
Problem Set 5
Cichello: FA 13
Problem Set 5
Due: 5:00 pm, Saturday, October 26th
The graded portion of this homework is found on MyStatLab . Answers to any questions
submitted after 5:00 pm on Saturday, October 26th will be given half credit.
P
Stats
Lecture 15: CLT, Proportions and Sampling
Distribution of Sample means
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If we draw a random sample from the population, we know that:
1. E[ ] =
x
2.
Var ( xi )
Var ( x )
n
3. Distribution of is a Normally distributed random variable (or ve
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Lecture 16: Sampling and Confidence Intervals
The Order in Chaos (DW): Catching Cheaters
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As the sample size gets large, the data will reveal its distribution and abnormalities become
obvious.
Example: Scores on a Polish Exam needed for Grad
Stats
Lecture 14: Sample Mean Distributions
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Distribution of Sample means
If we draw a random sample from the population, we find
1. E[ ] =
x
2.
Var ( xi )
Var ( x )
n
3. Under appropriate circumstances (described below), the distribution of sam
Stats
Lecture 17: Hypothesis Testing (known variance)
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Confidence intervals
If
x
~ N(,
), then a (1)% confidence interval will be:
2
x z / 2 x
x
 /2 refers to the area under the curve (or probability) to the right of the zvalue.
 For example,
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Lecture 18: Hypothesis testing with known and unknown variance
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Hypothesis Testing
Food as a share of total expenditures in South Africa
You know:
o Var(fs) = .04 (or .22)
o You arent sure if the underlying population is Normally distributed
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Lecture 13: Binomials as Approx. Normals & Sample Mean Distributions
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Normal Distributions
Finding x0 if Pr(X < x0) is given (or can be determined) and X has a known Normal distribution:
1. Start with the Standard Normal
a. Find the relevant
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Lecture 19: Working with tdistributions / Proportions
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Students t distributions
(Used when we do not know the variance in the underlying population distribution.)
If
x
is from a random sample and is Normally distributed, then
x
t
s/ n
~ t(
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Lecture 23: Power of a Test
Outcomes for a Hypothesis Test
Outcome of Hypothesis Test
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Actual Situation
Null is True
Null is False
Fail to reject null
CORRECT!
(1)
Type II error
()
Reject null
Type I error
()
CORRECT!
(1)
Power of a Test =
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Lecture 22: Proportions/Distribution of Sample Variance
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Sampling Distribution of the Sample Variance
1. Sample variances are random variables! (just like sample means are.)
2. Unfortunately, sample variances are not Normally distributed ran
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Lecture 20: Proportions/Distribution of Sample Variance
Confidence intervals when variance is unknown:
x t( n 1), / 2 x
OR
x t( n 1), / 2
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s
n
where t(n1),/2 is the t value that leaves /2 area under the curve in the right tail of a tdf=n1
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Lecture 24: Simple Regression
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Lecture 24
 Consulting Problem
(Finishing Power of a Test)
Fraud detection (with cost considerations)
 Bivariate Linear Regression Model
Regression as conditional expectation
Model components
o Equation form
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Lecture 26: Multiple regression
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Lecture 26

Does race play a role in Boston elections?
o Walsh and the minority vote in 2013 Mayoral election
How much of an increase in applications should BC expect if we win on Saturday?
o Data from BC, 1
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Lecture 27: Quadratic relationships and dummy variables
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Lecture 27

Should I really stay in school or just drop out now?

Gender discrimination in Thailand?

Benefits of travelling abroad
What we really are doing

Multiple Regression
o
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Suggestions for what to do when
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What should I do before class?
Nothing is required.
Many people prefer to read the textbook material for that day before the lecture so that
the lecture makes more sense. Others read it afterwards. Find what
Stats
Lecture 7: Discrete Random Variables
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Discrete Random Variables: How the house makes money! 4 coin toss example
Scenario 1: You get $1 for head & pay $1 for tail. xi represents your total payout
heads
0
1
2
3
4
xi
$4
$2
$0
$2
$4
P(X = xi)
Stats
Lecture 8: Binomial & Joint Distributions
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Bernoulli Random Variables: Only take on values 0 or 1
Scenario 1: X1 = 1 if sale to first customer; X1 = 0 otherwise. Makes sale 10 percent of time.
xi
P(X1 = xi)
P(xi)*xi
P(xi)*(xix)2
0
1
1.0
Sce
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Lecture 11: Uniform and Standard Normal Distributions
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Last note on Jointly Distributed Discrete Random Variables
Why did the Binomial distribution have E[X] = nP and Var(X) = nP(1P)?
where X is the sum of n independent random variables, pi
Statistics
Problem Set 4 SOLUTIONS
Cichello: FA 13
SOLUTIONS
Problem Set 4
Ch. 5: Continuous Random Variables
1) Uniform Distribution
a. If a random variable, X, has a uniform distribution over the values 10 to 15, what
does f(x) equal? Draw the diagram.
EC151.02: Statistics
EXAM 2
Spring 2013
Print Name:
This is an open book and open note exam. You may use a calculator. You may NOT use a phone
or a computer.
Please show sufficient work and formulas so that the instructor and TAs can follow your work.
Fai
Statistics
Problem Set 4
Cichello: FA 13
Problem Set 4
Due: 5:00 pm, Tuesday, October 15th
The graded portion of this homework is found on MyStatLab . Answers to any questions
submitted after 5:00 pm on Tuesday October 15 will be given half credit.
Please
EC151.02: Statistics
EXAM 2 SOLUTIONS
Spring 2013
SOLUTIONS
EXAM 2
Question 1: Basketball (27 pts.)
You are a college coach. During summer, you help run an elite summer league where only top
high school players are invited to play. During the camp, each
EC151.02: Statistics
EXAM 1 SOLUTIONS
Spring 2013
EXAM 1 SOLUTIONS
Unless otherwise indicated, each subpart of a question is worth 5 points.
Question 1: Hotdogs, drinks, and charity (10 pts.)
Suppose you organized a charity event held to help those affe
Statistics
Problem Set 5 SOLUTIONS
Cichello: FA 13
SOLUTIONS
Problem Set 5
Chapter 5 leftovers
1) Exponential Distribution (Why working together beats working alone.)
Your statistics homework is difficult. It takes some time to figure out how to go about
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Lecture 3: Variance, Covariance, Correlation, etc.
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Means Technical meanderings:
n
x
i
x i 1
n
Useful facts that feel useless at the moment, but will be used shortly.
1.
n
x
nx
i
i
1
2.
and
n
x
x i 1
n
3.
n
(x
i
1
xi
n i 1
n
i
i
1
x
n
x
Stats
Lecture 2: Reg to Mean, Descriptive Stats
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Seeing what others cannot see
Selection Bias: Airplanes in WW II
Airplanes returning from the front lines in WW II were examined. The bullet holes in the planes
were documented and analyzed. The sug
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Lecture 1: How to Fast Track your Career
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Introductions
My bio is on my website so I will not repeat it here.
How to Fast Track your career
1. Maintain: Be on time with your product
2. Excel: Be much more precise when others are vague
3. Exc
Stats
Lecture 5: Probability
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Notes on Permutations and Combinations (in reading):
1. You should be able to understand that order matters to permutations and does not in
combinations.
2. You should be able to calculate them if you are given the fo