Test II Review Sheet for
Colorado State University, Pueblo
Math 156 — Introduction to Statistics — Fall 2014

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
  1. population
  2. sample
  3. parameter
  4. statistic
  5. simple random sample [SRS}
  6. stratified random sample
  7. bias
  8. lurking variable
  9. voluntary response bias
  10. undercoverage
  11. observational study
  12. experiment
  13. treatment
  14. subjects
  15. randomization
  16. control
  17. placebo [effect]
  18. [double]-blind
  19. informed consent
  20. institutional review board [IRB]
  21. probability model
  22. sample space
  23. outcome
  24. event
  25. continuous/discrete RV
  26. disjoint
  27. sum rule for probabilities
  28. A or B for events A and B
  29. fair [die or coin]
  30. population distribution
  31. sampling distribution
  32. Law of Large Numbers [LoLN]
  33. Central Limit Theorem [CLT]
  34. independent events
  35. product rule for probabilities
  36. A and B for events A and B
  37. conditional probability
  38. tree diagram for conditional probabilities
  39. binomial scenario
  40. binomial RV and its distribution, mean, and standard deviation
  41. n factorial: $n!$
  42. n choose k: $\begin{pmatrix}n\\k\end{pmatrix}$
  43. normal approximation to the binomial

Things to know how to do

  1. discuss possible sources of bias and propose lurking variables in an experiment
  2. to investigate specific questions, propose experimental designs which will reduce bias and avoid ethical pitfalls
  3. analyze a proposed experimental design
  4. use the LoLN and the CLT in situations with sampling and to compute probabilities of certain average (or total) values of an RV
  5. 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
  6. compute conditional probabilities, verify and use independence of events
  7. recognize a binomial setting and compute binomial RVs where appropriate (using your calculator and the Normal approximation, if appropriate)

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
Chapter 13:   23, 25, 35, 39, 41
If you can do all of the above problems, you will do extremely well on the test.