MATH STAT TRIVIAL PURSUIT
(SORT OF)
FOR REVIEW
(MATH 30)
COLORS AND CATEGORIES
Blue – Basics of Estimation
 Pink – Properties of Estimators and Methods for
Estimation
 Yellow – Hypothesis Testing
 Brown – Bayesian Methods
 Green – Regression
 Orange – Nonparametric Procedures and
Categorical Data Analysis

BLUE 1

Suppose you have an estimator theta-hat, and
you want to know its bias. How is bias computed?
BLUE 2

How is MSE of an estimator computed?
BLUE 3

What is a common unbiased point estimator for a
population mean and what is its standard error?
BLUE 4

What is a common unbiased point estimate of a
difference in two population proportions, and
what is its standard error?
BLUE 5

A very important result related to samples from a
normal distribution is that:
The sample mean is ____________ distributed.
 The sample variance, appropriately scaled, is
____________ distributed.
 The sample mean and sample variance are
____________________.


(Fill-in all three blanks for credit).
BLUE 6

What are the 2 properties of pivot quantities and
what are pivots used for?
BLUE 7

How would you use the asymptotic normal
distribution of many unbiased point estimators to
create a confidence interval for their respective
parameters?

(You can just give the formula).

Hint: Think of a specific case and generalize.
BLUE 8

How is a t distribution formed?
BLUE 9

How is an F distribution formed?
BLUE 10

How do you form a small-sample confidence
interval for a population mean?
PINK 1

If relative efficiency is computed between two
estimators, it means that both estimators were
_______________, and if the numerical value of
the relative efficiency is 2, then it means that the
_____________ (first or second) estimator is
better.
PINK 2


What is the definition of consistency for an
estimator?
Bonus: What concept of convergence is this
equivalent to?
PINK 3


For an unbiased estimator, what is the “fast” way
of showing consistency?
Bonus: Do you remember what convergence
result this was derived from?
PINK 4

If you have a RS of n observations from a
distribution with unknown parameter theta, and
T is sufficient for theta, what does that mean?
PINK 5

What is the result you can use to show sufficiency
without resorting to computing conditional pdfs?
PINK 6


What does the Rao-Blackwell Theorem say?
Bonus: What’s the fast way of finding the
quantity RB refers to in the end?
PINK 7

Describe how the method of moments works.
PINK 8

Describe how the method of ML estimation
works.
PINK 9

A main property of MLEs is that they are
_____________, which means that ….
PINK 10


If an estimator is NOT admissible (i.e.
inadmissible), what does that mean?
Give an example of an inadmissible estimator.
YELLOW 1

What is the difference between simple and
composite hypotheses?
YELLOW 2

Describe the relationships between the two types
of error in a hypothesis test, as well as their
connection to power.
YELLOW 3

If you have a test statistic, you can use either a
rejection region approach or a p-value approach
to determine if the null hypothesis should be
rejected. What is the difference in the 2
approaches? (Describe).
YELLOW 4


For the common large sample asymptotically
normal z-tests, what is the rejection region for a
2-tailed test?
Bonus: If the significance level is .05 for this test,
what is the range of test statistics where you
would NOT reject the null hypothesis (numerical
values).
YELLOW 5

How are hypothesis tests and confidence
intervals related?
YELLOW 6

What is the difference between the pooled and
unpooled t-tests for 2 independent samples when
considering tests for means?
YELLOW 7

In order to determine which 2-sample t-test for
small sample sizes is appropriate, you might
have to run a test to check for equality of
_______________, and in order to control your
overall significance level, you might have to use a
____________ _____________.
YELLOW 8


What does the Neyman-Pearson Lemma say?
(Get the gist of it, what does it let you find, and
how?)
YELLOW 9

How do you determine if a most powerful test is
UMP?
YELLOW 10


How do you construct a likelihood ratio test?
What is the asymptotic distribution related to
LRTs?
BROWN 1

What is the major difference between Frequentist
and Bayesian approaches to statistics in terms of
how the parameter theta is treated?
BROWN 2


What is the difference between a proper and
improper prior?
What is the difference between an informative
and uninformative prior?
BROWN 3

How do you find the posterior density of theta?
BROWN 4

What are conjugate priors?

Give an example of a conjugate prior.
BROWN 5

How would you find the Bayes estimate of:
theta
 theta(1-theta)

if you had the posterior density of theta?
BROWN 6

A Bayes estimator is ALWAYS a function of a
_______________ statistic because of the
_______________ ________________.
BROWN 7

How is a Bayesian credible interval different
from a Frequentist confidence interval?
BROWN 8

Is it possible for Bayesian and Frequentists
intervals to agree? If yes, how might this happen?
BROWN 9

Bayesian hypothesis testing is performed using ______
________, which are Bayesian analogues of ________ test
procedures, and which can allow you to find evidence in
favor of your ___________ hypothesis.
BROWN 10

What are some of the issues related to working
with Bayes’ factors?
GREEN 1

Relationships between two variables, X and Y can
be deterministic or ________________. Regression is
used when the relationship is _______________. This
means that ….
GREEN 2

When first developing regression models, this is
the only constraint on the error terms.
GREEN 3

If your regression model was:
E (Y )   0  1 x1   2 x2  3 x3

Then how many parameters do you need to
estimate?
GREEN 4


In least squares solutions for regression, what
quantity is minimized to find the solution?
(You can just give the simple LR quantity).
GREEN 5

The least squares estimates are all ____________,
and their variances are functions of
_____________, which in turn can be estimated by
_______, which is equal to (1/(n-2))SSE.
GREEN 6

What is the full set of conditions on the error
terms in order to get normal sampling
distributions for the parameter estimates if
sigma is known?
GREEN 7

Why do we end up using a t distribution for
inference about slope parameters in regression
instead of a normal distribution?
GREEN 8

What is the main difference between a confidence
interval for a mean response and a prediction
interval for an individual response in regression?
GREEN 9

How are CIs for mean responses and prediction
intervals for individual responses affected as the
chosen x moves further from the mean of the x’s?
GREEN 10

What is correlation and how do we test about it?
ORANGE 1

Describe the two-sample shift model.
ORANGE 2

Describe how the sign test works.
ORANGE 3

Describe how the signed rank test works.
ORANGE 4

Describe how the Wilcoxon Rank Sum/MannWhitney U test works.
ORANGE 5

How does a Kolmogorov-Smirnov one-sample test
work? Is the null hypothesis in the procedure
simple or composite?
ORANGE 6

How does the 2-sample Kolmogorov-Smirnov test
work?
ORANGE 7

When performing categorical data analysis, the
main distribution you need to understand for the
theoretical setup of problems is the
______________ distribution, but the test
statistics turn out to have a different
distribution, which is the ________________
distribution.
ORANGE 8

How is a chi-square goodness of fit test
performed? When should you perform one?
ORANGE 9

How (and when) does a chi-square test of
independence work?
ORANGE 10

For 2x2 tables, inference is also possible with:
_________ exact test for small sample sizes
 _________ ratios, which relies on an asymptotic
______ distribution for it’s natural log.

REMINDER:
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
Takehome Final Exam is due Friday, May 13th at 5 p.m.
SHARP.
Office Hours (see front cover of exam):

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
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Monday 9-12 during my other course’s exam
Tuesday 10-12
Wednesday 1-3
Thursday 1-3
Any other time by appt. – just send me an email!
THANKS FOR A GREAT SEMESTER!
Math
dept. end of semester
picnic is Saturday from 12-2 at
the Alumni House