Review Sheet for Test II, Fall 2016
Colorado State University, Pueblo
Math 156 — Introduction to Statistics

Definitions

Terms you should know -- be able to state clearly what they mean, recognize them in examples, and create your own examples of them
  1. informed consent, "do no harm", anonymity/confidentiality, and institutional review board [IRB].
  2. observational study vs experiment
  3. bias and [its main preventative medicine:] randomization
  4. treatment and treatment group
  5. control group, Placebo Effect, and placebo
  6. blind[ing] and double-blind[ing]
  7. RCTs
  8. the sampling distribution
  9. simple random sample [SRS]
  10. block design [for sampling]
  11. volunteer sample bias
  12. the Central Limit Theorem [CLT]
  13. confidence intervals [CIs] (for the population mean with known and unknown population standard deviation and for the population proportion); particularly the meaning of the confidence level of a CI
  14. the margin of error [MoE] [of a CI]
  15. Student's $t$-distribution and degrees of freedom [for a sample]
  16. most conservative estimate [of the sample size needed for a CI for the population proportion with given MoE]
  17. hypothesis testing, the null and alternative hypotheses $H_0$ and $H_a$
  18. one- and two-tailed test
  19. test statistic, $z$- and $t$-statistic
  20. $p$-value of a hypothesis test; significance level for deciding when to reject $H_0$ or to fail to reject $H_a$.

Things to know how to do

  1. given a description of an experiment with human subjects, discuss if it meets our ethical guidelines OR design an experiment on human subjects that would be judged as ethical
  2. given a description of an experiment, discuss its design against the criteria of the gold standard, an RCT with double-blindness OR come up with an experiment design to investigate a particular question which comes as close as possible to the gold standard
  3. know when and how to use the CLT to determine the parameters of the sampling distribution in a particular situation and therefore also how to compute probabilities $\overline{X}$ will lie in certain ranges
  4. construct CIs for population means with known and unknown population standard deviations and for population proportions
  5. determine the sample size needed for CIs with given target MoE
  6. use Student's $t$-distribution appropriately
  7. do well-formed and -explained hypothesis testing; see this HT summary
  8. always, always, always, explaining your work clearly and completely, mixing explanation with calculation, and justifying each step of your work

Format of the test

Problems will be of a level of difficulty and wording similar to those on homework and quizzes. There will also be one problem with some information to interpret as if for an ASE. The total points for the test will be well more than 100, you can choose which 100 points you want to do out of the available problems. This means you should definitely choose to do first the problems about which you are the most confident, only coming back for the rest after finishing your first pass through the entire test.

This was a bit of an issue on Test I, so approach Test II wisely, not freaking out at how long it is but instead using time efficiently and calmly doing 100 points worth of problems.

Don't forget your calculator or whatever electronic tool[s] you like and notes or books to consult. While you can consult notes, you should always do so simply to make certain you have the right formula or you are checking all of the appropriate conditions — you should know the general shape of all the formulæ, results, and definitions.

Also in recent work students have been using on-line tools to do a lot of their work for them. While this is OK, you must always explain what the tool is doing, what it's inputs, outputs, and methods are, why it got the answer it did, how the answer would change in different situations, and what the answer means.

How to Study

It might be a good idea to put together all of your Big Ideas, review them, and make sure you know all of the things they describe. Make sure you can make a CI, determine the minimal sample size for a target MoE in a CI, and do a hypothesis test. Make sure you can explain the meanings of the confidence level of a CI and of the $p$-value of a hypothesis test. Make sure you know what an SRS is and can tell if a given sampling scheme will result in one, and you know in which of our methods it is necessary to work only with an SRS.

Go over your quizzes and HW problems and make sure you know how to do those kinds of things, and that you could do them again and get perfect scores on them now. If you want more problems, try doing other problems in the books which are near and similar to the ones which were assigned. If you do odd problems, you can check the answer is correct — but remember that the answer is not the important part, it is the explanation which is important. Maybe practice writing good solutions with complete explanations and justifications of every step.

Look at your ASEs and make sure you know how you could change them so that you would get a better score (if that is possible).