Review Sheet for the Final Exam, Fall 2015
Colorado State University, Pueblo
Math 156 — Introduction to Statistics

Prior Material

Remember the final exam is comprehensive, meaning that the material from all parts of the course will be covered, roughly in proportion to the course time we spent on it. Therefore it is important to review and be comfortable with all the material summaries in the review sheets for each of the course midterms, being Midterm I, Midterm II, and Midterm III.

New Terminology

Since Midterm III, we have seen
  1. the $t$ distribution with certain number of degrees of freedom ($df=n-1$ in a sample of size $n$)
  2. standard error
  3. confidence intervals for $\mu$ when $\sigma$ is unknown
  4. the $t$ statistic, used in the $t$ test [being a test of significance for $\mu$ when $\sigma$ is unknown]
  5. population proportion $p$
  6. sample proportion $\hat{p}$
  7. the large-$n$ distribution of $\hat{p}$
  8. confidence interval for a population proportion $p$
  9. the plus-four confidence interval for $p$

New Things to know how to do

The same structure as before requires new formulæ to compute
  1. a confidence interval for $\mu$ when $\sigma$ is unknown, using the $t$ distribution (with correct $df$),
  2. the $p$-value of a hypothesis test for $\mu$ with unknown $\sigma$, using the $t$ distribution (with correct $df$),
  3. a confidence interval for the population proportion $p$,
  4. a plus-four confidence interval for $p$, and
  5. the $z$-statistic in a hypothesis test for $p$.

There are new assumptions (in addition to the usual one, often the most important!, that the sample is an SRS) for using these methods:

  1. use $t$ distribution methods when the data is not too skew and had no bad outliers if $n\ge15$, or if $n\ge40$, it is even ok if the data is quite skew, and
  2. (for a plus-four CI for the population proportion $p$) the confidence level is 90% or higher, and $n\ge10$, and
  3. you can use the regular CI for $p$, without plus-four, if $n\hat{p}\gt15$ and $n(1-\hat{p})\gt15$
  4. (for reliable Hypothesis Tests for $p$) $np_0\ge10$ and $n(1-p_0)\ge10$.

Format and content of the final exam

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 final will be more than 200, you can choose which 200 points you want to do out of the available problems; try to do a full 200 points worth, since that is the maximum.

Your best guide to which topics will be covered in the final exam is the three midterms and the most recent homework (for the last part of the course which was not covered in any midterm). If you can do problems like these without hesitation and accurately, you will do fine on the final exam.

Just to remind you of those topics, they certainly include the following:

  1. Descriptive statistics, including
  2. working with the Normal distribution
  3. experimental design
  4. experimental ethics
  5. probability
  6. confidence intervals
  7. hypothesis tests

You may bring one page of notes to the final, written on one side. It should be in your handwriting and may contain general information but no examples — so, with the same restrictions (except for size) as the formula card for midterm III [don't forget that you may not put the explanations of the meaning of confidence level and $p$-value on your page of notes [although you will certainly be asked to give those explanations on the final — they must be in your head!]]. You will hand in this page with your test.

The final exam is Tuesday, 8 December 2015, 8-10:20am in our usual classroom.

Don't forget your calculator, you will need it!