AP Statistics Content Tips

Specific Statistics Content Tips

The following set of tips are things that are most worth remembering about specific content issues in statistics. These are things that have been consistent over the years of the reading. This list is not exhaustive! The examples, exercises, and solutions that appear in this book are illustrative of the manner in which you are expected to answer free-response problems, but this list is just a sampling of some of the most important things you need to remember.

1. When asked to describe a one-variable data set, always discuss shape, center, and spread in context. That means your answer should mention the variable and include units.

2. If you are asked to compare distributions, use phrases such as greater than, less than, and the same as. And, again, always answer in context.

3. Understand how skewness can be used to differentiate between the mean and the median.

4. Know how transformations of a data set affect summary statistics.

5. Be careful when using “normal” as an adjective. Normal refers to a specific model, not the general shape of a graph of a data set. It’s better to use “mound-shaped and symmetric,” etc., instead. You will be docked for saying something like, “The shape of the data set is normal.” No data set is exactly normal. At least, call it “approximately normal.”

6. Remember that a correlation does not necessarily imply a causal relationship between two variables. Conversely, the absence of a strong correlation does not mean there is no relationship (it might not be linear).

7. Be able to use a residual plot to help determine if a linear model for a data set is appropriate. Be able to explain your reasoning.

8. Recognize that the correlation coefficient (r) measures the strength and direction of a relation we have reason to believe is linear. The correlation coefficient does NOT tell us that the linear model is an appropriate model.

9. Be able to interpret, in context, the slope and y-intercept of a least-squares regression line. Be sure to include “predicted” or “tends to” in your description.

10. Be able to read computer regression output.

11. Know the definition of a simple random sample (SRS).

12. Know the definition of, and reasons for, choosing to do a stratified random sample instead of a simple random sample.

13. Be able to design an experiment using a completely randomized design. Understand that an experiment that utilizes blocking cannot, by definition, be a completely randomized design.

14. Explain the difference between the purposes of randomization and blocking.

15. Be able to describe what blinding and confounding variables are.

16. Clearly describe how to create a simulation for a probability problem.

17. Be clear on the distinction between independent events and mutually exclusive events (and why mutually exclusive events can’t be independent).

18. Be able to find the mean and standard deviation of a discrete random variable.

19. Recognize binomial and geometric situations.

20. Never forget that hypotheses are always about parameters, never about statistics.

21. Any hypothesis testing procedure involves four steps. Know what they are and that they must always be there. And never forget that your conclusion in context (Step 4) must be linked to your calculations (Step 3) in some way.

22. When doing inference problems, remember that you must show that the conditions for the inference procedure are present. It is not sufficient to simply declare them present. Realize that you are often not instructed to check the conditions in the question but you must do so anyway.

23. Be clear on the concepts of Type I and Type II errors and the power of a test.

24. If you are required to construct a confidence interval, remember that there are three things you must do to receive full credit: justify that the conditions necessary to construct the interval are present; construct the interval; and interpret the interval in context. You’ll need to remember this, because often the only instruction you will see is to construct the interval.

25. If you include graphs as part of your solution, be sure that axes are labeled and that scales are clearly indicated. This is part of communication.

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