AP Statistics: An Apex Learning Guide: 2003-2004 / Edition 2

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Overview

With AP Statistics, you'll go into the exam with confidence. AP Statistics comes complete with a targeted review of the test material, two full-length practice tests plus hundreds of practice questions, and Kaplan's exclusive test-taking strategies. This powerful combination makes AP Statistics a highly effective way for you to score higher.
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Product Details

  • ISBN-13: 9780743241526
  • Publisher: Kaplan Publishing
  • Publication date: 3/1/2003
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 672
  • Product dimensions: 8.44 (w) x 10.92 (h) x 1.75 (d)

Table of Contents

Section I The Basics
Chapter 1 Inside the AP Statistics Exam 3
Chapter 2 Strategies for Succeeding on the Exam 9
Section II Statistics Review
Chapter 3 Describing Data 25
Practice Questions 59
Chapter 4 The Normal Curve 127
Practice Questions 145
Chapter 5 Bivariate Data: Regression Analysis and Two-Way Tables 183
Practice Questions 220
Chapter 6 Planning a Study 263
Practice Questions 273
Chapter 7 Probability 307
Practice Questions 322
Chapter 8 Sampling Distributions and Binomial Problems 367
Practice Questions 377
Chapter 9 Hypothesis Testing 407
Practice Questions 422
Chapter 10 The t Distribution for Means 455
Practice Questions 472
Chapter 11 Inference for Proportions 525
Practice Questions 533
Chapter 12 Chi-Square and Inference for Least-Squares Lines 559
Practice Questions 583
Section III Practice Tests
Practice Test One 601
Answers and Explanations 623
Practice Test Two 633
Answers and Explanations 655
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First Chapter

Chapter 1 Inside the AP Statistics EXamBefore you plunge into studying for the AP Statistics exam, let's take a step back and look at the big picture. What's the AP Statistics exam all about? How can you prepare for it? How's it scored? This chapter and the next will answer these questions and more. What is the Advanced Placement (AP) Program? Through the Advanced Placement Program, you can take college-level courses while you are in high school. Based on your grade on an AP Exam, colleges and universities can grant you placement or college credit or both. In addition to getting a head start on your college coursework, you can improve your chances of acceptance to competitive schools since colleges know that AP students are better prepared for the demands of college courses. There's also the money you can save on tuition if you receive credit! Structure of the AP Statistics Exam The AP Statistics exam is administered in May by the College Board's AP Services. The exam is three hours long, so developing your stamina is very important. The exam consists of two equally weighted sections: Section I -- Multiple-Choice, and Section II -- Free-Response. Section I -- Multiple-Choice There are 40 multiple-choice questions. Each multiple-choice question is worth 1 point. Section II -- Free-Response The second section of the examination consists of 4 to 7 open-ended questions and an investigative task. Each open-ended question is designed to be answered in approximately 10-15 minutes, depending on how many there are. The investigative task is longer and is designed to be answered in 25-30 minutes. There's a five-minute break between Section I and Section II. AP Statistics Exam at a Glance Number of Time Calculator Questions (minutes) Permitted? Section I (multiple choice) 40 90 Yes Section II (free response) Open-ended questions 4-7 60 Yes Investigative task 1 30 Yes Calculators and Computers You will not have access to a computer during the AP Statistics exam. However, standard computer output may be provided as part of the exam, and you will be expected to be able to interpret it. You will need to bring a graphing calculator with statistical capabilities to the exam. Your calculator's capabilities should include: € Computation of descriptive statistics, such as the standard deviation, correlation coefficient, and least-squares linear regression equations € Graphing of scatterplots, boxplots, histograms, and least-squares linear regression lines It is also useful if your graphing calculator has a spreadsheet-like format for entering data. The TI-83, made by Texas Instruments, is one example of an appropriate calculator for the AP Statistics exam. You are not allowed to use a calculator with a QWERTY keypad because it makes it too easy to type text (such as test questions) into the calculator. Topic Outline for AP Statistics The breakdown of the AP Statistics exam covers the four main themes outlined below. The chapters of this book which review those content areas are also listed. 1) Exploring Data -- chapters 3, 4, 5 Exploring univariate data: interpreting graphical displays, summarizing and comparing distributions, measuring centers -- median, mean, measuring spread -- range, interquartile range, standard deviation, measuring position -- quartiles, percentiles, standardized scores Exploring bivariate data: patterns in scatterplots, correlation and linearity, least squares regression line, residual plots, outliers, and influential points, transformations to achieve linearity Exploring categorical data: frequency tables, including marginal and joint frequencies for two-way tables 2) Planning a Study -- chapter 6 Data collection: census, sample survey, experiment, observational study Planning and conducting surveys: simple random sampling, conducting a well-designed survey, sampling error, sources of bias Planning and conducting experiments: confounding, control groups, placebo effects, blinding, treatments, experimental units, randomization, experimental design, replication and generalizability 3) Probability and Simulation -- chapters 7 and 8 Probability: relative frequency, law of large numbers, rules of probability, conditional probabilities, independence, discrete and continuous random variables, binomial and geometric distributions, mean and standard deviation Normal distribution: properties, using tables, central limit theorem Simulations: sampling distributions, sample proportion, sample means, difference between two proportions, difference between two means 4) Statistical Inference -- chapters 9, 10, 11, 12 Confidence intervals: for proportions, for means, for difference between two proportions, for difference between two means Tests of significance: null and alternative hypotheses, p-values, one-and two-sided tests, large sample tests for proportions, means, difference of proportions, difference of means, chi-square test for goodness of fit and independence Normally distributed data: t-distribution, single-sample t procedures, two-sample t procedures (independent and matched pairs), inference for slope of least squares lines Scoring the AP Statistics Exam The AP Statistics exam is scored on a scale of 1 to 5, with 5 being the highest grade. The scores are defined as follows: 5 Extremely well qualified 4 Well qualified 3 Qualified 2 Possibly qualified 1 No recommendation In 2000, the average grade of the 34,118 candidates who took the AP Statistics test was 2.69. Keep in mind that each college decides for itself which AP scores will be accepted for advanced placement or college credit. Many schools award one semester of placement or credit for a score of 3 or higher on the AP Statistics exam, but some schools might require a 4 or 5, and there are a few schools that do not accept AP scores at all. It would not be correct to say that the AP examination is graded "on the curve." How other students do on the same exam will not affect your score. However, some multiple-choice questions are used from one year to the next to allow for a calibration of the scores, ensuring that scores reflect the same statistical strength of performance each year. For this reason, the cut-offs for each score level do not stay constant from year to year. How Are Exams Graded? The multiple-choice section of the exam is graded by computer. The free-response section is graded by faculty consultants -- college professors and AP teachers who are specially trained to assess the questions. Students' names and schools are concealed on the free-response booklets to ensure fairness in the grading process. Scoring the Multiple-Choice Questions For multiple-choice questions, there is a penalty for answering incorrectly, as opposed to simply leaving an item blank. (This is sometimes called a guessing penalty, but it is really a wrong answer penalty. If you guess correctly, you're in great shape!) Here's how the scoring works: You receive 1 point for a correct answer, 0 points for no answer, and -1/4 point for a wrong answer. For example, getting 30 correct and 10 wrong would give you a score of 30 - (10¥1/4) = 27.5. We'll talk more about guessing on the AP Statistics multiple-choice section in the next chapter. Scoring the Free-Response Questions The free-response questions are graded holistically, meaning that the graders evaluate your answer as a total package rather awarding partial credit for separate parts of your work. A four-point scale is used (0-4 points possible) on each question. A grader evaluating the quality of your work bases the score on two things: 1) Statistical knowledge: Have you identified the important components of the problem? Have you demonstrated correct statistical concepts and techniques that result in a correct solution? 2) Communication: How well have you explained what you have done and why? Have you clearly stated the conclusions that you have drawn? Here are the general guidelines that graders consider when scoring AP Statistics free-response questions: How Do I Get My Grade? AP Grade Reports are sent in July to each student's home, high school, and any colleges designated by the student. Students may designate the colleges they would like to receive their grade on the answer sheet at the time of the test. Students may also contact AP Services to forward their grade to other colleges after the exam, or to cancel or withhold a grade. AP Grades by Phone AP Grades by phone are available for $15 a call beginning July 1. A touch-tone phone is needed. The toll-free number is (888) 308-0013. Registration To register for the AP Statistics exam, contact your school guidance counselor or AP Coordinator. If your school does not administer the exam, contact AP Services for a listing of schools in your area that do. Fees The fee for each AP Exam is $80. The College Board offers a $22 credit to qualified students with acute financial need. A portion of the exam fee may be refunded if a student does not take the test. There may be a late fee for late exam orders. Check with AP Services for applicable deadlines. Additional Resources The College Board offers a number of publications about the Advanced Placement Program, including: Advanced Placement Program Course Description -- Statistics, A Guide to the Advanced Placement Program, and the AP Bulletin for Students and Parents. You can order these and other publications online at store.collegeboard.com, or call AP Services for an order form. For More Information For more information about the AP Program and/or the AP Statistics exam, contact your school's AP Coordinator or guidance counselor, or contact AP Services at: The study of government and politics is enhanced by the use of an analytic approach with which to explain relationships and behavior. No single approach is necessarily the best or the most definitive, nor does any single approach satisfactorily explain all aspects of U.S. government. By using an analytical approach, however, one acquires a consistent understanding of the relationships among actors and institutions, and an explanation for outcomes and policy results. Listed below are the major categories to consider when examining U.S. government and politics. Keep in mind that these are not commensurable variables. 1. Actors are individuals or groups that seek to obtain goals through political activity and policymaking. 2. Interests are the values that people hold. These might be economic, social or philosophical, or political values. These fuel the actions and efforts of actors in politics. 3. Institutions involve the formal organizations that exercise political power. Congress, the president, the courts, and the bureaucracy are all institutions that develop and implement public policy, as formally outlined in the Constitution. Less formal institutions also play a significant role in government and politics. These include political parties, interest groups, and the mass media. Considered to be linkage institutions rather than formal, governmental institutions, they focus on the accomplishment of a goal in the political system, in that they convey citizens' interests to government. 4. Processes are the steps that various actions, that is, policy proposals, must go through to approach formal public policies. This is the way the policymaking institutions formally consider policy proposals. 5. Outcomes are the actual results of these components. Outcomes may be in the form of an adopted formal policy, or they may be no action and a continuation of the status quo. Their impact and consequence on policy are an important feature of politics and government. Various analytic perspectives could explain U.S. government and politics. Each may contribute to understanding, though none is a completely adequate or satisfactory perspective. Government involves the institutions and processes by which public policies are made for a society. Politics is connected to questions of who gets what, when, and how. Politics produces an authoritative allocation of values in our society. Elitism is based on the idea that political decisions and power are controlled by a small elite of powerful, often rich, individuals. This perspective posits that society is divided along class lines, based on wealth and tradition, and upper-class elites rule, regardless of whatever else appears to be taking place. Pluralism posits that policy is the product of group conflict and that the public interest tends to emerge from competing individual and group claims as they bargain and compromise. No single interest can dictate the outcome; people must compromise or form coalitions in order to attain their goals. Hyperpluralism is an extreme form of pluralism. A hyperpluralistic government is so fragmented, and pressures from competing interest groups are so diverse, that very little gets done. The result is often gridlock. The political system provides a "systemic" view of relationships between individuals, interests, institutions, and policy decisions. It explains politics in terms of: € inputs (the demands and supports from individuals or intermediate groups); € processing of these inputs by the formal institutions of government; € outputs (the policies set forth by the government); and € feedback (from outputs to the actors). Power is the ability to cause others to modify their behavior. It is a constant feature of government and politics, though power is quite unevenly distributed among actors and institutions. This perspective views actors and actions in terms of what interests possess what power, and how that power influences governmental actions. A political culture underlies the behavior of Americans and the values they have within the political system. These values serve as the context in which politics takes place, and though they are not homogeneous across the country, there is a degree of uniformity that underlies most political actions and behavior. Key Terms and Concepts aristocracy A system of government in which control is based on rule of the highest class. capitalism An economic system based on individual and corporate ownership of the means of production and a supply-demand market economy. communism A political, economic, and social theory based on the collective ownership of land and capital and in which political power lies in the hands of workers. conservative One who believes in and supports the typically traditional values of conservatism, and who resists change in the status quo. democracy A system of government placing the ultimate political authority in the people. Derived from the Greek words demos (the people) and kratos (authority). direct democracy A system of government in which the people, rather than elected representatives, directly make political decisions. This system is probably possible only in small political communities. free market economy The economic system in which the invisible hand of the market regulates prices, wages, and production. gridlock A situation in which government is incapable of acting on important issues often because of divided government. indirect (or representative) democracy A system of government that gives citizens the opportunity to vote for representatives who will work on their behalf. liberal A person slightly to the left of the center of the political spectrum who believes that change is good. Today's liberals tend to believe that the government has a role in preserving individual freedoms and equality, and in solving social and economic problems. libertarian One who favors a free market economy and no governmental interference in personal liberties. majority rule The central idea of governance in which only policies that have the support of a majority of voters will be made into law. minority rights Protections that guarantee that the minority will not be destroyed because they favor policies or actions different from the majority. monarchy A form of government in which power is vested in a monarch, an hereditary king and/or queen. oligarchy A form of government in which the right to participate is limited to those who possess wealth, social status, military position, or achievement. personal liberty A fundamental characteristic of democracy in the United States that protects individuals from government intrusion or interference. political culture Political beliefs and attitudes concerning government and political process held by a group of people, such as a community or nation. political ideology The collectively held ideas and beliefs concerning the nature of the ideal political system, economic order, social goals, and moral values. politics The method in which decisions are made, either by or for a society, to allocate resources, distribute benefits, and impose costs. Politics is a difficult term to define and has been summed up in many ways, including: "the art of the possible," the "authoritative allocation of values," "who gets what, when, and how" in a society, and "the competition among individuals and groups over the allocation of values or rewards." popular consent The idea that government must draw its powers from the governed or the people who are sovereign. popular sovereignty A principle originating in natural rights philosophy that claims political authority rests with the people and not the government. People have the right to create, change, or revolt against their government. In practice, people usually choose representatives to exercise their political authority. republic A government in which ultimate sovereignty belongs to the people, and the people elect officials to represent them in government decisions. social contract A basic tenet of liberal democracy that people are free and equal by natural right and therefore people give their consent to government. Advocated by John Locke and reflected in the Declaration of Independence. socialism A political philosophy that supports government control of markets and production as well as government determination of peoples' needs for social and economic benefits. totalitarianism A philosophy of politics that advocates unlimited power for the government so that it controls all sectors of society. Multiple-Choice Questions 1. All of the following characteristics are features of the pluralist analytic perspective except I. A multiplicity of institutional access points II. A diverse and numerous set of actors with competing policy objectives III. Changing coalitions of actors IV. A single process for making policy outcomes A. I and II B. II and III C. III and IV D. III E. IV 2. Political participation is an essential element of all of the following approaches except A. the political system. B. elitism. C. pluralism. D. power. E. hyperpluralism. 3. The value or importance of an analytic framework in understanding politics and government is that A. it predicts results of the process. B. it explains all dimensions of politics and government. C. it encompasses all the variables that might account for policy outcomes. D. it provides a comprehensive and systematic perspective of politics. E. it results in the disclosure of truth. 4. Initiatives and referenda are examples of A. direct, popular government. B. Republicanism. C. political party control. D. oligarchy. E. indirect democracy. 5. Popular sovereignty can be defined as A. translation of legislation into a set of government programs and policies. B. the level of popular support that presidents enjoy from approval surveys. C. the influence that public opinion polls have in deciding policy questions. D. the right of the majority to govern themselves. E. the idea that governments draw authority from the governed. Essay Questions 1. List three variables that pluralism uses to explain politics. Then, list three variables that elitism uses in explaining politics. Compare and contrast these two approaches in terms of democratic policy making. 2. Select one approach below and identify at least three strengths and one weakness it has for studying government and politics. € Elitism € Pluralism € the Political System ANSWER KEY Multiple-Choice Questions 1. E 2. B 3. D 4. A 5. D Essay Questions 1. Variables that could be listed for the pluralist approach to explaining politics include: € Many interest groups with specialized or narrow interests € Competition among interests for governmental attention € A number of policy making institutions € Various processes for influencing policy making Elitist variables might include: € Powerful, concentrated policy makers, usually based on economic power € Members of the elite are strongly and actively engaged in politics as well as ideologically committed to their interests € Elite members may or may not occupy elected positions in order to control policies € There are interlocking connections among the members of the elite so the same actors appear in various policy making contexts The question does not specify the number of comparisons and contrasts required, so a general statement of comparison and contrast is probably sufficient. Comparisons: 1. Both approaches provide a comprehensive perspective for explaining politics and policy results. 2. Both approaches tie institutions to actors and to results (policies). Contrasts: 1. Pluralism is a more complicated explanation for policy outcomes than is elitism: pluralism involves more actors, and both winners and losers, and they cannot be easily predicted by pluralists beforehand. 2. Elitism is a more simplistic approach to explaining politics because everything is the result of the presence of a controlling elite. 2. This question asks you to identify three strengths and one weaknesses of one approach. Make sure that you do precisely that, or your answer will be incomplete.
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