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.