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 sigma² 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.