Test II Review Sheet for
Colorado State University, Pueblo
Math 156 — Introduction to Statistics —
Spring 2015
PLEASE NOTE:
Several students had issues on Quiz 8 which need to be straightened out before
the test. The way to do this is by reviewing the material in Chapter 12,
particularly on conditional probability and checking if events are independent,
and making sure you can make nice Venn diagrams (see, e.g., Example 12.5
on p. 312 of your textbook).
All students who were in class to take the quiz should have received an answer
sheet by e-mail; if you did not, e-mail me and I will respond with the answer
sheet. Also, a number of recent classes have been filmed: the ones with a small
camera icon next to that date on the HW web page. If you would like a link to
one of those videos, just e-mail me.
Definitions/Theorems
Terms and statements you should know -- be able to state clearly what they
mean, recognize them in examples, and create your own examples of them
- population
- sample
- parameter
- statistic
- simple random sample [SRS}
- stratified random sample
- bias
- lurking variable
- voluntary response bias
- undercoverage
- observational study
- experiment
- treatment
- subjects
- randomization
- control
- placebo [effect]
- [double]-blind
- informed consent
- institutional review board [IRB]
- probability model
- sample space
- outcome
- event
- continuous/discrete RV
- disjoint
- sum rule for probabilities
- A or B for events A and B; also $A\cup B$
- fair [die or coin]
- population distribution
- sampling distribution
- Law of Large Numbers [LoLN]
- Central Limit Theorem [CLT]
- independent events
- product rule for probabilities
- A and B for events A and B; also $A\cap B$
- conditional probability
- Venn diagram for computing probabilities from given information
- tree diagram for conditional probabilities
Things to know how to do
- discuss possible sources of bias and propose lurking variables in an
experiment
- to investigate specific questions, propose experimental designs which
will reduce bias, create a randomized, controlled, double-blind
situation, and avoid ethical pitfalls
- analyze a proposed experimental design for effectiveness and ethical
considerations (being informed consent, IRB, confidentiality, "do no
harm"
- use the LoLN and the CLT in situations with sampling and to compute
probabilities of certain average (or total) values of an RV
- given an description of a situation with randomness, define an appropriate
sample space, compute probabilites of given events and their combinations,
and compute the distribution of a given RV
- compute conditional probabilities, verify and use independence of events
Format of the test
There will be several problems from the material corresponding to each chapter
we've done in the textbook, of a level of difficulty and wording similar to
the problems which you have done for homework and quizzes. The total points
for the test will be more than 100, you can choose which 100 points you want
to do out of the available problems.
You may bring one page — written on only one side! — of notes to
the test. It should be in your handwriting and may contain any general
information you like: no examples, but any general formula or algorithm
or statement you like. You will hand in this page with your test, and it will
be returned with your graded test.
Don't forget your calculator, you will need it!
Practice Problems
You should absolutely be able to do all of the homework problems which were
assigned in class. In addition, the following problems are extra practice you
could do if you like. Remember, providing complete, detailed explanations of
your work is the largest part of your work, it is not an optional add-on.
| Chapter 8: |
27, 35, 39 |
| Chapter 9: |
31, 39, 45, 47 |
| Data Ethics: |
1, 5, 11 |
| Chapter 10: |
31, 41, 43, 47, 53 |
| Chapter 11: |
25, 27, 31, 35, 39 |
| Chapter 12: |
35, 37, 39, 41, 53 |
If you can do all of the above problems, you will do extremely well on the test.