AP Statistics All Access

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Chapter 1

Welcome to REA’s All Access for AP Statistics

A new, more effective way to prepare for your AP exam.

There are many different ways to prepare for an AP exam. What’s best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

This book, and the web and mobile tools in the All Access package, will help you personalize your AP prep by testing your understanding, pinpointing your weaknesses, and delivering flashcard study materials unique to you.

Let’s get started and see how this system works.

How to Use REA’s AP All Access

The REA AP All Access system allows you to create a personalized study plan through three simple steps: targeted review of exam content, assessment of your knowledge, and focused study in the topics where you need the most help.

Here’s how it works:

Finding Your Weaknesses: The REA Study Center

The best way to personalize your study plan and truly focus on your weaknesses is to get frequent feedback on what you know and what you don’t. At the online REA Study Center, you can access three types of assessment: topic-level quizzes, mini-tests, and a full-length practice test. Each of these tools provides true-to-format questions and delivers a detailed score report that follows the topics set by the College Board.

Topic-Level Quizzes

Short, 15-minute online quizzes are available throughout the review and are designed to test your immediate grasp of the topics just covered.

Mini-Tests

Two online mini-tests cover what you’ve studied in each half of the book. These tests are like the actual AP exam, only shorter, and will help you evaluate your overall understanding of the subject.

Full-Length Practice Test

After you’ve finished reviewing the book, take our full-length exam to practice under test-day conditions. Available both in this book and online, this test gives you the most complete picture of your strengths and weaknesses. We strongly recommend that you take the online version of the exam for the added benefits of timed testing, automatic scoring, and a detailed score report.

Improving Your Score: e-Flashcards

Once you get your score report, you’ll be able to see exactly which topics you need to review. Use this information to create your own flashcards for the areas where you are weak. And, because you will create these flashcards through the REA Study Center, you’ll be able to access them from any computer or smartphone.

Not quite sure what to put on your flashcards? Start with the 100 free cards included when you buy this book.

After the Full-Length Practice Test: Crash Course

After finishing this book and taking our full-length practice exam, pick up REA’s Crash Course for AP Statistics. Use your most recent score reports to identify any areas where you are still weak, and turn to the Crash Course for a rapid review presented in a concise outline style.

REA’s Suggested 8-Week AP Study Plan

Depending on how much time you have until test day, you can expand or condense our eight-week study plan as you see fit.

To score your highest, use our suggested study plan and customize it to fit your schedule, targeting the areas where you need the most review.

Test-Day Checklist

Chapter 2

Strategies for the Exam

What Will I See on the AP Statistics Exam?

One May morning, you stroll confidently into the school library where you’re scheduled to take the AP Statistics exam. You know your stuff: you paid attention in class, followed your textbook, took plenty of notes, and reviewed your coursework by reading a special test prep guide. You can identify and describe graphs, design experiments, and interpret test results. So, how will you show your knowledge on the test?

The Multiple-Choice Section

First off, you’ll complete a lengthy multiple-choice section that tests your ability to not just remember facts about the various fields of statistics, but also to apply that knowledge to interpret and analyze statistical information. This section will require you to answer 40 multiple-choice questions in just 90 minutes. Here are the major fields of inquiry covered on the AP Statistics exam:

Graphing and describing univariate, bivariate, and categorical data

Experimental design and sampling methods

Probability

Simulations

Inference procedures

So being able to name which type of sampling method was used if every tenth person was surveyed entering a basketball game (systematic, but you know that, right?) will not do you much good unless you can also explain how accurate sampling methods prevent bias and provide representative samples. It sounds like a lot, but by working quickly and methodically you’ll have plenty of time to address this section effectively. We’ll look at this in greater depth later in this chapter.

The Free-Response Section

After time is called on the multiple-choice section, you’ll get a short break before diving into the free-response section. This section requires you to produce six written responses in 90 minutes. Like the multiple-choice section, the free-response portion of the exam expects you to be able to apply your own knowledge to analyze data, in addition to being able to provide essential facts and definitions.

What’s the Score?

Although the scoring process for the AP exam may seem quite complex, it boils down to two simple components: your multiple-choice score plus your free-response scores. The multiple-choice section accounts for one-half of your overall score and is generated by awarding one point toward your raw score for each question you’ve answered correctly. The free-response section accounts for the remaining one-half of your total score. In this section, questions one through five count equally to make up three-eighths of your final score, and question six is weighted to count for one-eighth of your final score. Trained graders will read students’ written responses and assign points according to grading rubrics. The number of points you accrue out of the total points possible for each question will form your score on the free-response section.

The test maker reports AP scores on a scale of 1 to 5. Although individual colleges and universities determine what credit or advanced placement, if any, is awarded to students at each score level, these are the assessments typically associated with each numeric score:

5 Extremely well qualified

4 Well qualified

3 Qualified

2 Possibly qualified

1 No recommendation

Section I: Strategies for the Multiple-Choice Section of the Exam

Because the AP exam is a standardized test, each version of the test from year to year must share many similarities in order to be fair. That means that you can always expect certain things to be true about your AP Statistics exam.

Which of the following phrases accurately describes a multiple-choice question on the AP Statistics exam?

¹

What does this mean for your study plan? You should focus more on the application and interpretation of the various analytical fields of statistics than on nuts and bolts such as formulas and finding P-values, because content makes up a much larger portion of the exam. Also, the required formulas will be provided to you on the test, and you will have access to your calculator. Keep in mind, too, that many statistical concepts overlap. This means that you should consider the connections among ideas and concepts as you study. This will help you prepare for more difficult interpretation questions and give you a head start on questions that ask you to use Roman numerals to organize ideas into categories. Not sure what this type of question might look like? Let’s examine a typical Roman numeral item:

Which of the following statements accurately applies to the boxplots shown above?

I. The range is the same for both graphs.

II. Twenty-five percent of dataset 1 is equal to or greater than 50 percent of dataset 2.

III. There are more data points in dataset 1.

IV The first quartile for dataset 1 is greater than the median for dataset 2.

Types of Questions

You’ve already seen a list of the general content areas that you’ll encounter on the AP Statistics exam. But how do those different areas translate into questions?

Throughout this book, you will find tips on the features and strategies you can use to answer different types of questions.

Achieving Multiple-Choice Success

It’s true that you don’t have a lot of time to finish this section of the AP exam. But it’s also true that you don’t need to get every question right to get a great score. Answering just two-thirds of the questions correctly—along with a good showing on the free-response section—can earn you a score of a 4 or 5. That means that not only do you not have to answer every question right; you don’t even need to answer every question at all (although there is no penalty for wrong answers so you should answer every question). By working quickly and methodically, however, you’ll have all the time you’ll need. Plan to spend about two minutes and 15 seconds on each multiple-choice question. You may find it helpful to use a timer or stopwatch as you answer one question to help you get a handle on how long 135 seconds feels in a testing situation. Remember that you will be able to answer some questions very quickly while others will take longer. If timing is hard for you, set a timer for 33 minutes each time you take one of the online chapter-level quizzes that accompany this book, to help you practice working at speed. Let’s look at some other strategies for answering multiple-choice items.

Process of Elimination

You’ve probably used the process-of-elimination strategy, intentionally or unintentionally, throughout your entire test-taking career. The process of elimination requires you to read each answer choice and consider whether it is the best response to the question given. Because the AP exam typically asks you to find the best answer rather than the only answer, it’s almost always advantageous to read each answer choice. More than one choice may have some grain of truth to it, but one—the right answer—will be the most correct. Let’s examine a multiple-choice question and use the process of elimination approach:

A group of researchers wants to find out if freshmen or seniors in high school are more flexible. They design a flexibility test that assigns to each student a flexibility score from 1 to 100. The researchers then administer the test to a random sample of freshmen and seniors attending the local high school. Which of the following would be an appropriate method to test the hypothesis that freshmen and seniors are equally flexible?

Students often find the most difficult question types on the AP exam to be those that ask you to find a statement that is not true or to identify an exception to a general rule. To answer these questions correctly, you must be sure to carefully read and consider each answer choice, keeping in mind that four of them will be correct and just one wrong. Sometimes, you can find the right answer by picking out the one that just does not fit with the other choices. If four answer choices relate to characteristics associated with quantitative data, for example, the correct answer choice may well be the one that relates to categorical data. Let’s take a look at a multiple-choice question of this type.

The following can be said about a well-designed, completely randomized experiment EXCEPT:

Predicting

Although using the process of elimination certainly helps you consider each answer choice thoroughly, testing each and every answer can be a slow process. To help answer the most questions in the limited time given AP test takers, you may find it helpful to instead try predicting the right answer before you read the answer choices. For example, you know that the answer to the math problem two-plus-two will always be four. If you saw this multiple-choice item on a math test, you wouldn’t need to systematically test each response, but could go straight to the right answer. You can apply a similar technique to even complex items on the AP exam. Brainstorm your own answer to the question before reading the answer choices. Then, pick the answer choice closest to the one you brainstormed. Let’s look at how this technique could work on a common type of question on the AP Statistics exam—one with computer output.

Students at one university are convinced that taking tests while hungry has adverse effects on test scores. The students take a census of their statistics class by asking their classmates to rate their hunger level on a scale from one (starving) to ten (full), and then having the professor match the hunger level with the test score results anonymously. The students wish to create a 95-percent confidence interval for the slope. The computer output is listed below:

A computer output question will rarely ask you simply to read a piece of information from the output. Instead, you will need to apply what you have learned about statistics to interpret the information provided. You can use your knowledge of statistics to make good predictions to answer these types of questions. Always take a moment to study the computer output (or graph) before diving into the question.

In this example, notice that the output shows that the slope is 0.053649. It also shows that the standard error for the slope is 0.375363. So you already know that the answer is going to be 0.053649 ± t* (0.375363). You can then use the inverse t function on your calculator to find the correct answer: 0.053649 ± 1.6759(0.375363). Now you can look at the answer choices and quickly pick your answer from the list.

A) 35.22547 ± 1.6759(1.45889)

B) 35.22547 ± 0.142927(0.375363)

C) 0.053649 ± 1.6759(1.45889)

E) 0.053649 ± 0.142927(0.375363)

What should you do if you don’t see your prediction among the answer choices? Your prediction should have helped you narrow down the choices. You may wish to apply the process of elimination to the remaining options to further home in on the right answer. Then, you can use your statistical knowledge to make a good guess.

Learning to predict takes some practice. You’re probably used to immediately reading all of the answer choices for a question, but in order to predict well, you usually need to avoid doing this. Remember, the test maker doesn’t want to make the right answers too obvious, so the wrong answers are intended to sound like appealing choices. You may find it helpful to cover the answer choices to a question as you practice predicting. This will ensure that you don’t sneak a peek at the choices too soon.

Sometimes, though, you need to have a rough idea of the answer choices in order to make a solid prediction, especially when there are lots of possible ways to interpret a question. Let’s examine another question to practice predicting in this way.

When performing a hypothesis test, which of the following will give you the greatest power?

Before looking at the answer choices you would think to yourself: To increase power I can increase sample size, increase α, or move H0 further away from where I think the actual value is. You know that the larger the sample size, the higher the power, but you are not going to arbitrarily start guessing sample sizes. You can now look at the answer choices and quickly see that (D) is the correct answer because it has the largest sample size and the largest alpha value.

A) n = 200, α = 0.01

B) n = 200, α = 0.05

C) n = 600, α = 0.01

E) Cannot be determined.

Avoiding Common Errors

Remember, answering questions correctly is always more important than answering every question. Take care to work at a pace that allows you to avoid these common mistakes:

Missing key words that change the meaning of a question, such as not, except, or least. You might want to circle these words in your test booklet so you’re tuned into them when answering the question.

Overthinking an item and spending too much time agonizing over the correct response.

Changing your answer but incompletely erasing your first choice.

Some More Advice

Let’s quickly review what you’ve learned about answering multiple-choice questions effectively on the AP exam. Using these techniques on practice tests will help you become comfortable with them before diving into the real exam, so be sure to apply these ideas as you work through this book.

Big ideas are more important than minutiae. Focus on learning important statistical concepts, models, and theories instead of memorizing formulas.

You have just 135 seconds to complete each multiple-choice question. Pacing yourself during practice tests and exercises can help you get used to these time constraints.

Because there is no guessing penalty, remember that making an educated guess is to your benefit. Remember to use the process of elimination to narrow your choices. You might just guess the correct answer and get another point!

Instead of spending valuable time pondering narrow distinctions or questioning your first answer, trust yourself to make good guesses most of the time.

Read the question and think of what your answer would be before reading the answer choices.

Expect the unexpected. You will see questions that ask you to apply information in various ways, such as picking the wrong idea or interpreting a graph, table, or computer output.

Section II: Strategies for the Free-Response Section of the Exam

The AP Statistics exam always contains six free-response questions in its second section. This section always allows you 90 minutes to respond to all six of these questions. Often, these questions provide you with one or more visual stimuli, such as tables, computer output,