Statistics Unit 4 Review
Ophelia Gurin
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The AP Statistics exam includes 40 multiple-choice questions and 6 free-response questions, including one Investigative Task; the Investigative Task is simply a challenging free-response question that applies the material to a new context.
The College Board has released two full AP Statistics Exams: 2012 AP Statistics Exam and 1997 AP Statistics Exam. Because they often reuse multiple choice questions, they limit the number of full official tests they make public (you can supplement this with full-length practice exams from Albert). For free response questions, the College Board has released twenty years of official AP questions to be used for practice and review. Hooray!
This question proves that a formula sheet is not necessarily your golden ticket to a 5. While you are provided a formula sheet for the test, the writers for the AP Statistics Exam need to know that you can do more than plug-and-chug numbers. They want to know if you understand when and how to use each formula. This problem is a perfect example of how they might assess your knowledge of two-sample proportions and null hypotheses.
You need to remember that this test has the null hypothesis: p_1=p_2! That means we perform calculations under the assumption that the two groups are equal, or that the null is true. So, you need to combine the two samples (with 34 and 150 successes out of a total 800 adults) to find a combined proportion of success \hatp_c=0.23. Then, and only then, you can plug your values into the appropriate formula. The answer is D.
Quick tip: touch on all key features of the graphs using the acronym SOCS: shape, outliers, center, and spread. By talking about these features in context of the problem, you would be on track to earning an E (essentially correct) for part (a).
Many students will get this problem wrong by accidentally running a two sample t-test instead of a matched pairs t-test. What they fail to recognize is that the two groups (before and after) are dependent on the person, thus matched up! If you need practice identifying statistical methods, try this interactive applet on Classifying Statistics Problems.
Just based on length alone, you can tell that the Investigative Task is significantly longer than other free response questions. Luckily, you are budgeted more time (25 minutes) to parse through the question and deliver a quality response.
This problem demands a deep understanding of linear regression, dummy variables, and abstract thinking about the interaction of multiple variables. Looking at the scoring guidelines, you can see a focus on clear communication rather than long computations. So make sure to explain all your thinking and provide detailed explanations of your answers.
You should take your time in this self-assessment piece to really make the most of your study sessions. Read carefully through the free response scoring guidelines while grading yourself, even reading the notes and alternative solutions.
Afterwards, go through the topics list and highlight each item based on your level of understanding: green if you are highly confident in that topic, yellow if you are close to mastery, and pink for topics that you need to review and practice.
Find out how many days you have before the AP Statistics Exam day, and block out time each day for review. Even if you only review for 15 minutes a day, that is better than 8 hours of cramming the night before the exam. If you can, find a partner to join you for your study sessions!
*An important part of this process is checking your answers and reading through the solutions carefully. If you can articulate WHY you got an answer wrong and how your understanding of the topic has changed, you will be well on your way to acing the AP Statistics Exam.
Put your newfound knowledge to the test with another full test, paying careful attention to time management as you move through each section. You should budget about 2 minutes per multiple choice problem, 13 minutes for each regular free response, and 25 minutes for the Investigative Task. Afterwards, reflect on where you felt comfortable and rushed, and figure out exam sections that you may need to study up or save for last. For example:
The classic model involves setting a timer and studying for 25 min sessions with a 5 min break in between each session. You can take a longer (30 min) break after 4 sessions to keep your mind fresh and productive. This will truly make the study sessions fly by!
Instead of memorizing things that are already provided to you, you should reference each practice problem to a formula on the sheet (when applicable) and make a mental map of the cheat sheet. It is a similar process to annotating a book for close reading, where you write your own thoughts and opinions in the margins to help process and retain information.
Reading your textbook and gaining knowledge is one thing; putting that knowledge to the test with challenging practice questions is another. As soon as possible, start doing multiple choice and free response questions from College Board, Albert, or AP Statistics Review Books. We hope that you make mistakes and learn from them. Utilize your teachers and peers for help when you get stuck, then do as many practice problems as you can to build knowledge and confidence.
This is especially useful when it comes to calculating probabilities (with Venn diagrams or normal distributions), finding summary statistics for skewed distributions, and envisioning trends in scatterplots.
Remember than you have about 13 minutes for the standard free response questions, and 25 minutes for the Investigative Task. Keep track of your time and write down something for every part to ensure that you have as detailed an explanation as possible.
When test day finally comes, it is normal to feel a little jittery and anxious about the exam. Instead of last minute cramming, here are some tips and tricks for test day that will help you walk into the exam feeling confident!
If you get stuck on a problem, skip it and come back to it later. Give yourself time checks to get through each part of the exam, budgeting an extra 20 minutes at the end to check over your work, clarify explanations, and finish missing problems.
Other than some light review with flashcards, you should avoid heavy studying and do what you can to put your mind at ease on the morning of test day. Mimic an athlete on the day of a big race or game. Do some light stretches, eat a healthy breakfast, pump yourself up with positive messaging, and trust that your preparation will pay off come game time.
This site is created by a high school math teacher from Simi Valley, CA and provides concise summary notes + practice problems for each unit. In addition to AP Statistics, his site contains materials for Algebra, Geometry, AP Computer Science, and other math courses.
We hope you have found this review guide helpful. If you follow the advice in this article and walk into the exam with a positive attitude, we are 100% confident that you will be happy with your score. Good luck!
It can be tempting to jump prematurely into a statistical analysis when undertaking a systematic review. The production of a diamond at the bottom of a plot is an exciting moment for many authors, but results of meta-analyses can be very misleading if suitable attention has not been given to formulating the review question; specifying eligibility criteria; identifying and selecting studies; collecting appropriate data; considering risk of bias; planning intervention comparisons; and deciding what data would be meaningful to analyse. Review authors should consult the chapters that precede this one before a meta-analysis is undertaken.
An important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention. Potential advantages of meta-analyses include the following:
Of course, the use of statistical synthesis methods does not guarantee that the results of a review are valid, any more than it does for a primary study. Moreover, like any tool, statistical methods can be misused.
This chapter describes the principles and methods used to carry out a meta-analysis for a comparison of two interventions for the main types of data encountered. The use of network meta-analysis to compare more than two interventions is addressed in Chapter 11. Formulae for most of the methods described are provided in the RevMan Web Knowledge Base under Statistical Algorithms and calculations used in Review Manager (documentation.cochrane.org/revman-kb/statistical-methods-210600101.html), and a longer discussion of many of the issues is available (Deeks et al 2001).
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