AP Statistics: With 6 Practice Tests

As you review the content in this book and work toward earning that 5 on your AP STATISTICS exam, here are five things that you MUST know:

1. Graders want to give you credit—help them! Make them understand what you are doing, why you are doing it, and how you are doing it. Don’t make the reader guess at what you are doing.
   • Communication is just as important as statistical knowledge!
   • Be sure you understand exactly what you are being asked to do or find or explain and approach each problem systematically.
   • Some problems look scary on first reading but are not overly difficult and are surprisingly straightforward. Questions that take you beyond the scope of the AP curriculum will be phrased in ways that you should be able to answer them based on what you have learned in your AP Statistics class.
   • Naked or bald answers will receive little or no credit. You must show where answers come from.
   • On the other hand, don’t give more than one solution to the same problem—you will receive credit only for the weaker one.
2. Random sampling and random assignment are different ideas.
   • Random sampling is the use of chance in selecting a sample from a population and is critical in being able to generalize from a sample to a population.
     • A simple random sample (SRS) is when every possible sample of a given size has the same chance of being selected.
     • A stratified random sample is when the population is divided into homogeneous units called strata, and random samples are chosen from each strata.
     • A cluster sample is when the population is divided into heterogeneous units called clusters, and a random sample of the clusters is chosen.
     • A systematic sample is when a random starting point is followed by choosing every kth member of a list.
   • Random assignment in experiments is when subjects are randomly assigned to treatments and is critical in minimizing the effect of possible confounding variables.
     • This randomization evens out effects over which you have no control and allows for a valid comparison of treatments.
     • Randomized block design refers to when the randomization occurs only within groups of similar experimental units called blocks.
3. Distributions describe variability, and variability is the most fundamental concept in statistics. Understand the difference between:
   • population distribution (variability in an entire population),
   • sample distribution (variability within a particular sample), and
   • sampling distribution (variability between samples).
   • The larger the sample size, the more the sample distribution looks like the population distribution.
   • Central Limit Theorem: the larger the sample size, the more the sampling distribution (probability distribution of the sample means) looks like a normal distribution.
4. Choosing the correct procedure and performing proper checks are critical.
   • Categorical variables lead to proportions or chi-square procedures, while quantitative variables lead to means or linear regression.
   • Decide whether there is a single population of interest or two populations being compared.
   • Know the proper checks for each procedure and state them correctly. (Listing wrong conditions will lose points.)
   • Verifying assumptions and conditions means more than simply listing them with little check marks—you must show work or give some reason to confirm verification.
5. Calculating the P-value is not the final step of a hypothesis test.
   • There must be a decision to reject or fail to reject the null hypothesis.
   • You must indicate how you interpret the P-value; that is, you need linkage. So, “Given that P = 0.007, I reject …” isn’t enough. You need something like, “Because P = 0.007 is less than 0.05, there is sufficient evidence to reject …”
   • The conclusion must refer to the population and be in the context of the problem.
   • Reemphasizing from #1 above: Communication is just as important as statistical knowledge!