Chapters 6 & 7: Most important concepts

1. The **normal distribution** -- A *theoretical* frequency distribution that is a good
model for the distribution of errors (including *sampling error*) and many other
variables

2. Interpretation of **area under the curve** in a **normal distribution** as the
probability of scores within a certain range.

3. A **sampling distribution** of
means: the
set of x-bars that would be obtained for all
possible random samples of size *n*

4. The **central limit theorem** (CLT),
which
tells us the sampling distribution will
have µ = µ, **standard error** _{}= sigma /sqrt
*n* and will become normal as *n* goes to
(infinity)

5. CLT allows us to determine how likely it is that a particular sample mean comes from a population with mean µ.

Chapter 8: Most important concepts

1. The CLT allows us to ask questions about *populations* using *samples*.

2. The 5 steps of *hypothesis testing* (step 5
is
answering the research question in
English)

3. The *null hypothesis* provides an
"anchor" for
our sampling distribution.

4. The difference between *Type I error*,
which
we control when we choose , and
*Type II error*, which depends on the *power *of the hypothesis test.

What it means to *reject* the null (you've
detected a difference) or *fail to reject* the
null hypothesis (you didn't find an effect)

Chapter 9: Most important concepts

1. When the population variance is unknown, we can't
use
a z-test, and must use a *t-test*.

2. When sigma^{2} is unknown, we must
*estimate
it* using the sampling variance, which uses
*n*-1 to correct bias

3. There's a* family* of
t-distributions. The shape and proportions of the t-distribution
vary based on df, the degrees of freedom. t becomes normal as df gets large.

4. To use the t-test, either the underlying population must be normal or you need
large *n *(30 is large).

5. T-test assumes that the variance of both known and unknown population is the same.

Key Skills from Chapters 6 - 8:

1. Use the unit normal table

2. Calculate standard error, which tells us how good a measurement is of µ

3. Locate a sample mean in a sampling distribution, by finding its z-score and using the unit normal table

4. Given µ & sigma for a known population, and
x-bar
and *n* for a sample from an unknown
population, test the hypothesis that µ for the unknown population = µ for known
pop.

a. Turn a research question into a null and alternative hypothesis

b. Identify critical values and region

c. Calculate the z test statistic

d. Compare b&c to make decision about null

e. Translate this into an answer (in English) to the research question

Key Skills from Chapter 9:

1. Distinguish between situations calling for z-test and or for a single sample t-test

2. Compute the estimated standard error.

3. Compute the degrees of freedom.

4. Compute the t-statistic.

5. Use the t distribution table on page A-27. Pay attention to degrees of freedom to get the right row, and then pick the column based on your alpha and number of tails.