Test III Review Sheet for
Colorado State University, Pueblo
Math 156 — Introduction to Statistics — Spring 2015

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. confidence interval (for a population mean $\mu$)
  2. confidence level
  3. margin of error [MoE]
  4. critical value $z^*$
  5. test of significance or hypothesis test (for a population mean $\mu$)
  6. null hypothesis vs alternative hypothesis
  7. test statistic or $z$-statistic
  8. one-tailed or one-sided test vs two-tailed or two-sided test
  9. $p$-value
  10. significance level
  11. type I error and type II error

Things to know how to do

  1. compute a confidence interval (for a population mean $\mu$) at a particular confidence level
  2. make a MoE larger or smaller by changing the confidence level or sample size
  3. determine the sample size to get a particular MoE
  4. explain the meaning of the confidence level of a confidence interval
  5. set up the null and alternative hypotheses for a particular applied problem (for a population mean $\mu$)
  6. compute the $z$-statistic for a hypothesis test
  7. compute the $p$-value, using the appropriate formula (one out of the three possible) depending upon the alternative hypothesis
  8. explain the meaning of the $p$-value of a test of significance

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 standard size index card — written on only one side! — of formulæ to the test. It should be in your handwriting and may contain only the following kinds of information:

In particular, this means that you may not put the language which you will use to explain confidence levels and $p$-values on your formula card: you need to get this into your head.

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 14:   9, 11, 13, 22, 23, 25
Chapter 15:   3, 5, 7, 15, 17, 21, 31, 39, 41
Chapter 16:   13, 19, 41
If you can do all of these problems, all of the actually assigned homework problems, and all of the recent quizzes, without difficulties or mistakes, you will do extremely well on the test.