2004
QE1 Statistics Review
Adam Shrager
ashrager@yahoo.com
ashrager@princeton.edu
April 4, 2004
First, the disclaimer…
 I have not seen this year’s exam
 Everything is subject to change
 Consider the following direction in the realm
of highly probabilistic based on prior (recent)
exams.
 In terms of focusing your studying
efforts…there are some pretty clear
guidelines….
The three types of Statistics
Questions on the QE1
 The Regression Question
– Explain the model
– Calculate something
– Analyze or criticize the model
 The Hypothesis Testing Question
– Often difference of means or proportions
– Your choice: Confidence interval or t-test
 The Probability Question
– On May ’03 exam.
– Bayes Rule (Conditional Probability)
The Regression Question
1. Explain the Regression Equation
What are we modeling? Restate dependent and
independent variables.
What does one additional unit of X do to Y?
Get specific.
May ’02:
“ A one mpg increase in avg. fuel efficiency will lower
the per capita oil consumption by 0.38 barrels per
person per year.”
The Regression Question
 Plug numbers into the model to solve for
something.
May ’02:
3 mpg increase lowers oil consumption by 1.14
barrels per person per year (0.38 x 3). With 260
million people, change in national oil
consumption would be 296 million barrels per
year (260,000,000 x 1.14). Question asked for
you to explain the 296 million barrel claim.
The Regression Question
 Criticize/Analyze/Discuss the model
– CORRELATION!!!!!!!
– External validity
– What else impacts Y?
 Use “external” knowledge (or knowledge gleaned
from background reading) here.
Hypothesis Testing
 Be prepared for:
– Difference of Means
– Difference of Proportions
Have these formulas handy!!!!!
Consider:
“Do I like confidence intervals or do I like t-tests?”
Hypothesis Testing
TIPS FOR SUCCESS
 Make and explicitly state your assumptions.
Even if wrong, then your answers will
logically flow.
 Assumptions:
– State Null (H0) and Alternative (Ha) hypothesis
– Two-sided/one sided test
– Level of confidence (often .05)
– What test are you using and why?
Hypothesis Testing
TIPS FOR SUCCESS
 Be sure to explicitly test for (and state that you are
testing for) the following:
– If confidence interval, is zero in the interval? Why does
this matter? (also common: if asking about “majority,” is
.50 in the interval?)
– If t-test, explicitly state critical value (often 1.96 or 1.68,
could be something else). Does your test statistic
exceed this value? What does that mean? Even if you
screw up the math – by explicitly stating what you’re
doing, the grader can follow your logic and may only
deduct nominal points.
– If you use both tests – do your answers correspond?
THEY SHOULD!!!!!!!!!
Probability
 What could they ask
you?
– Conditional Probability
 Bayes Rule.
– It’s your choice…..
Bayes Rule
 The algebraic formulation for Bayes’ Rule
 P (A│B) = P (B│A) P (A) / P (B)
(plug in the numbers presented to you as
appropriate, and solve)
Bayes Rule
 Much easier to solve with a tree.