Final Exam Review Sheet for
Colorado State University, Pueblo
Math 156 — Introduction to Statistics —
Spring 2015
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
- the $t$ distribution with certain number of
degrees of freedom ($df=n-1$ in a sample of size $n$)
- the $t$ statistic, used in the $t$ test
- population proportion $p$
- sample proportion $\hat{p}$
- the plus-four confidence interval
New Things to know how to do
The same structure as before requires new formulæ to compute
- a confidence interval for $\mu$ when $\sigma$ is unknown, using the $t$
distribution (with correct $df$),
- the $p$-value of a hypothesis test for $\mu$ with unknown $\sigma$,
using the $t$ distribution (with correct $df$),
- a confidence interval for the population proportion $p$,
- a plus-four confidence interval for $p$, and
- 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:
- 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
- (for a plus-four CI for the population proportion $p$) the confidence
level is 90% or higher, and $n\ge10$, and
- you can use the regular CI for $p$, without plus-four, if $n\hat{p}\gt15$
and $n(1-\hat{p})\gt15$
- (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:
- Descriptive statistics, including
- graphing data
- measures of center and spread
- outliers
- scatterplots
- correlation
- working with the Normal distribution
- symmetry
- using the table or calculator
- the 68-95-99.7-rule
- experimental design
- randomness
- bias
- placebos
- experiment vs observational study
- SRS
- lurking variable
- experimental ethics
- probability
- sample space, outcome, event
- independent, disjoint
- addition law, multiplication law
- conditional probability
- Venn diagrams
- distribution of an RV
- confidence intervals
- for $\mu$ (with and without known $\sigma$) and $p$
- confidence level -- be able to explain!
- margin of error
- conditions for applicability
- hypothesis tests
- for $\mu$ (with and without known $\sigma$) and $p$
- null and alternative hypotheses
- $p$-value -- be able to explain!
- significance level
- one-tailed and two-tailed tests
- type I and type II error
- conditions for applicability
You may bring one page of notes to the final, written on one side. 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.
The final exam is Tuesday, April 28th, 10:30am-12:50pm in our
usual classroom.
Don't forget your calculator, you will need it!