Review Sheet for Test III, Fall 2015
Colorado State University, Pueblo
Math 156 — Introduction to Statistics
Definitions/Concepts
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
- [population] parameter and [sample] statistic
- an unbiased statistic
- the Law of Large Numbers
- population distribution and sampling distribution
- confidence interval (for a population mean $\mu$)
- confidence level
- margin of error [MoE]
- critical value $z^*$
- test of significance or hypothesis test (for a population
mean $\mu$)
- null hypothesis and alternative hypothesis
- test statistic or $z$-statistic
- one-tailed or one-sided test vs two-tailed
or two-sided test
- $p$-value
- significance level
- statistically significant
- type I error and type II error, which are related to,
but not the same as false positive and false negative
Things to know how to do
- compute a confidence interval (for a population mean $\mu$) at a
particular confidence level
- make a MoE larger or smaller by changing the confidence level or sample
size
- determine the sample size to get a particular MoE
- explain the meaning of the confidence level of a confidence interval
- set up the null and alternative hypotheses for a particular applied
problem (for a population mean $\mu$)
- compute the $z$-statistic for a hypothesis test
- compute the $p$-value, using the appropriate formula (one out of the
three possible) depending upon the alternative hypothesis
- 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:
- equations or formulæ written with symbols
- definitions of those symbols such as, e.g., things like
"$\mu=$population mean."
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.
If you use a formula card, you must turn it in with your test. (But it will be
returned with your graded test so you can use it in the future.)
Don't forget your calculator, you will need it!