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5 Steps to a 5: 500 AP Statistics Questions to Know by Test Day (2020)

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    Downloaded from StudyXY.com [= Ww + StudyXY oi as . Za \ Rr ' BE \ Stu dy Anything This ContentHas been Posted On StudyXY.com as supplementary learning material. StudyXY does not endrose any university, college or publisher. Allmaterials posted are under the liability of the contributors. | 8) www.studyxy.com

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    Copyright © 2020, 2017, 2012 by McGraw-Hill Education. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-1-26-045980-7 MHID: ~~ 1-26-045980-2 The material in this eBook also appears in the print version of this title: ISBN: 978-1-26-045979-1, MHID: 1-26-045979-9. eBook conversion by codeMantra Version 1.0 All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com. McGraw-Hill Education, the McGraw-Hill Education logo, 5 Steps to a 5, and related trade dress are trademarks or registered trademarks of McGraw- Hill Education and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. McGraw-Hill Education is not associated with any product or vendor mentioned in this book. AP, Advanced Placement Program, and College Board are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, this product.

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    TERMS OF USE This is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL EDUCATION AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill Education and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill Education nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.

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    Introduction Chapter 1 Overview of Basic Statistics Questions 1-20 Chapter 2 One-Variable Data Analysis Questions 21-70 Chapter 3 Two-Variable Data Analysis Questions 71-120 Chapter 4 Design of a Study: Sampling, Surveys, and Experiments Questions 121-170 Chapter 5 Probability and Random Variables Questions 171-225 Chapter 6 Binomial Distribution, Geometric Distribution, and Sampling Questions 226-280 Chapter 7 Confidence Intervals Questions 281-330 Chapter 8 Inference for Means and Proportions Questions 331-390 Chapter 9 Inference for Regression Questions 391-445

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    Chapter 10 Inference for Categorical Data Questions 446-500 Answers

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    INTRODUCTION Congratulations! You’ve taken a big step toward AP success by purchasing 5 Steps to a 5: 500 AP Statistics Questions to Know by Test Day. We are here to help you take the next step and score high on your AP Exam so you can earn college credits and get into the college or university of your choice. This book gives you 500 AP-style questions that cover all the most essential course material. Each question has a detailed answer explanation that can be found at the back of the book. These questions will give you valuable independent practice to supplement your regular textbook and the groundwork you are already doing in your AP classroom. This and the other books in this series were written by expert AP teachers who know your exam inside out and can identify the crucial exam information as well as questions that are most likely to appear on the exam. You might be the kind of student who takes several AP courses and needs to study extra questions throughout the year. Or you might be the kind of student who puts off preparing until the last weeks before the exam. No matter what your preparation style is, you will surely benefit from reviewing these 500 questions, which closely parallel the content, format, and degree of difficulty of the questions on the actual AP exam. These questions and their answer explanations are the ideal last-minute study tool for those final few weeks before the test. Remember the old saying, “Practice makes perfect.” If you practice with all the questions and answers in this book, we are certain you will build the skills and confidence you’ll need to do well on the exam. Good luck! —Editors of McGraw-Hill Education

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    CHAPTER Overview of Basic Statistics 1. A student is conducting a survey of his classmates. In his questionnaire, he has asked for several factors, including the student’s race and gender. The student plans to use this data to conduct a regression on the impact of these variables on grades. The teacher has advised him to use a different set of variables. Why is it difficult to make any kind of meaningful calculations based on these two specific variables? (A) Because both gender and race are examples of quantitative data and such data is not suited for any kind of statistical analysis. (B) Because gender is an example of categorical data, while race is an example of discrete data, and it is not possible to use them in the same calculation. (C) Because gender is an example of discrete data, while race is an example of continuous data, and it is not possible to consider them both without including a dummy variable. (D) Because both gender and race are examples of continuous data and using them for meaningful calculations is not possible without performing some kind of statistical transformation. (E) Because both gender and race are examples of categorical data, and both of them can only be expressed as dummy variables, which makes them ill-suited for the student’s project. 2. Which of the following is an example of quantitative data? (A) Radiation levels in millirems of food in Japan

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    (B) Fashionable colors by season of the year (C) Gender (D) High school grade level-freshman, sophomore, junior, or senior (E) Favorite sport 3. Which of the following is an example of discrete data? (A) Lifetime (in hours) of 35 fluorescent light bulbs (B) Weights of dogs (in pounds) at the Seal Beach Animal Care Center (C) Temperature (in Fahrenheit) of the Pacific Ocean at Huntington Beach (D) Number of hamburgers sold each day at Hamburger Mary’s (E) Amount of caffeine (in milligrams) for 8 ounces of popular drinks 4. A stockbroker trading on the New York Stock Exchange is observing a report of changing values for the NASDAQ 100. Why is this an example of continuous data? (A) Because this data only has two binary options. (B) Because this data can only be qualitative. (C) Because it can take any measure within a certain range. (D) Because it can only be expressed as a dummy variable. (E) Because such data cannot be used for any kind of statistical analysis. 5. The Department of Justice is preparing a summary report of all crimes for 2018. Which of the following is a correct use of descriptive statistics to evaluate the dataset it is considering? (A) Trying to understand key reasons for the increase in the crime rate by using relevant psychological and sociological theories (B) Determining that the largest number of crimes in a larger city in the United States was 34 crimes per 1,000 residents (C) Conducting a literature review to project criminal trends in the future (D) Determining that the violent crime rate for 2019, based on a regressive projection, will be higher by 2%

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    (E) Conducting a high-low analysis to project the value of the 2019 murder rate 6. Choose the statement below that describes the use of inferential statistics. (A) The average grade on Test 3 in Spring Semester College Algebra was 63%. (B) “By assessing the coloration and state of health of 195 free-living urban pigeons, they found that darker pigeons had lower concentrations of a blood parasite called haemosporidian.” (C) U.S. Department of Education data from 2007-2008 found that KIPP charter schools received $12,731 per student. (D) The average age of students in Biology 101 is 23.5 years. (E) The standard deviation of the pain scores from the Tylenol treatment group was 1.25. 7. A company is preparing an investor’s report for the previous year. Why is making a regression projection for next year’s stock value an example of inferential statistics? (A) Because it makes a statistically relevant projection that always excludes the past trends of variables (B) Because it uses the mean of the dataset to make an educated guess about the value of the stock next year (C) Because it uses a combination of observing the minimum and maximum values to observe the data (D) Because it conducts an analysis of the existing dataset and provides a conclusion based on that data (E) Because it depends on understanding the existing literature to understand the trends in the stock market 8. Choose the statement below that describes a parameter. (A) Gallup poll on “life evaluation” showing 53% “thriving” and 44% “struggling” (B) Proportion of wrinkled peas in a sample collected in an organic garden (C) The standard deviation of the age of students attending

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    community college based on 10 representatives from each campus (D) Average salary of all professors at San Francisco City College (E) Average concentration of lactic acid in 30 samples of cheddar cheese from Cheddar Gorge, UK 9. A researcher is considering the impact of a virus that targets a particular strain of vegetables in three different locations around the globe. Elsewhere, a college professor is interested in finding out how popular a particular political candidate is. How are the research methods for these two scenarios different? (A) The most effective way of investigating the researcher’s dilemma is a survey, while the college professor should conduct a literature review. (B) The most effective way of investigating the researcher’s dilemma is an experiment, while the college professor should conduct a survey. (C) Both of them would receive the best results through conducting a survey of the general population. (D) The most effective way of investigating the researcher’s dilemma is a literature review, while the college professor should use some form of inferential statistics. (E) Both of them should make a regression model to make a statistically relevant projection. 10. Identify the situation where you would conduct a survey. (A) Gallup wishes to determine the proportion of people who see themselves as “thriving.” (B) Stanford researchers want to determine the effect that improving student vision has on learning. (C) A pharmaceutical company wants to advertise that its painkiller is more effective than aspirin, ibuprofen, and Tylenol. (D) A gambler wishes to calculate the expected value of buying two lottery tickets. (E) The U.S. Army wants to find the average cost of training a cadet. 11. Which of the following describes a random variable?

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    (A) The price of a barrel of crude oil on the commodities market on April 1, 1984 (B) The number rolled on a fair die (C) The grade earned on an exam by a student (D) The time required by Jaouad Gharib to run a marathon (E) The weight of a gallon of water 12. Why is randomization commonly used when selecting a sample? (A) To allow computers to aid in the process (B) So that only data relevant to the values of interest is collected (C) To avoid bias from being introduced (D) So that the sample is not taken from a group that is not related to the question of interest (E) To aid in calculations of sample statistics 13. Which of the following measures the center of a distribution? (A) Standard deviation (B) Mean and median (C) Interquartile range and range (D) Variance (E) Correlation coefficient 14. Which of the following measures the spread of data? (A) Mean (B) Median and interquartile range (C) First and third quartiles (D) Correlation coefficient (E) Standard deviation and variance 15. A marketing agent is trying to determine how to best market a new line of smartphones in the United States. In order to do so, he needs to know what users currently like about the company’s products and where they require improvements. The agent’s key problems are that he has a limited budget and he needs to know current consumer preferences. Evaluate the best way for him to achieve the desired

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    result. (A) Conducting a detailed literature review of the existing literature (B) Conducting a survey of the market in the United Kingdom and using these findings to draw conclusions regarding the U.S. market (C) Conducting a survey of a representative sample of the U.S. population and using these findings to infer relevant conclusions (D) Using descriptive data to analyze past consumer preferences (E) Using previous sales data to make a multivariate regression model to project future preferences 16. What common sampling technique involves considering the population of interest as a collection of nonoverlapping groups and selecting from each of these groups? (A) Stratified sampling (B) Cluster sampling (C) Random sampling (D) Systematic sampling (E) Representative sampling 17. What is the purpose of the chart shown below?

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    (A) To identify the standard deviation of revenue compared to profit (B) To identify whether the mean profit is larger than the mode revenue (C) To make a multivariate projection of sales based on revenue and profit (D) To determine whether there is any correlation between revenue and profit (E) To observe whether there is any causation going from revenue to profit 18. To identify the shape of univariate data, what type of graph would be the most useful? (A) Cumulative frequency plot (B) Histogram (C) Scatter plot (D) Bar chart (E) Pie chart 19. Researchers studied the effects that improving vision with eyeglasses had on educational outcomes. They identified 2,069 students who could improve their vision with eyeglasses. Of these, 750 were not offered eyeglasses and 1,319 were. Of the 1,319 offered eyeglasses, 928 accepted the eyeglasses. Students who received the eyeglasses scored significantly higher in both math and science. Why was it significant for the researchers to have a group of students that did not have glasses? (A) By doing so, the researchers could have a control group that tested if the treatment of including the glasses was statistically significant. (B) Through the inclusion of such a group, the researchers had another dependent variable that impacted the overall results of the experiment. (C) The researchers could use these students to observe the students who were being treated, which is why they are an independent variable. (D) The researchers included them as an instrumental variable that

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    made the project invalid. (E) By including this group of students, the researchers wanted to introduce a dummy variable to ensure the validity of the project. 20. A linguist studied conversation styles by gender and age to assess differences between genders. The data were collected by studying videotapes made of “best friends” who were asked to have a conversation together. Which choice best describes the type of study that was conducted? (A) Observational (B) Experimental (C) Poll (D) Census (E) Survey

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    One-Variable Data Analysis 21. Describe the shape of the histogram below. (A) Normal (B) Bimodal (C) Skewed right (D) Skewed left (E) Uniform 22. Two college professors are grading several papers and are required to draw histograms to show the grade distribution at the end of the

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    semester. The test scores are graded on a range of 0 to 100 points. Which of the following claims is correct? (A) The exam results graded by the first professor have a right- skewed distribution because the median is different from the standard deviation. (B) The exam results graded by the second professor have a normal distribution because the mode and mean are equal. (C) The exam results graded by the first professor have a normal distribution because the mean, median, and average are the same. (D) The exam results for the first professor cannot be visually represented because two of the students achieved all of the points available. (E) The exam results for the second professor have a right-skewed distribution because the mode and mean are larger than the median. 23. If a researcher has drawn a histogram and he is observing one where the distribution is left-skewed, which of the following statements is most likely correct? (A) The median is to the left of the mean and the peak. (B) The mean is to the left of the median and the peak. (C) The mode is to the left of the median. (D) The mode is to the left of the mean. (E) The median and mean have the same value. 24. Find the mean and the median in the dot plot below (n = 20). (A) Mean: 12.9; median: 13

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    (B) Mean: 12.4; median: 13 (C) Mean: 12.9; median: 13.5 (D) Mean: 12.9; median: 14 (E) Mean: 12.4; median: 14 25. Find the number of data values represented and the median for the stem plot below. (A) n= 13; median: 36.5 (B) n= 20; median: 36.56 (C) n= 24; median: 32 (D) n= 13; median: 34 (E) n= 20; median: 34 26. Data values represented by the bar labeled “10” in the histogram below fall into which range?

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    (A) 7.5upto 12.5 (B) 7.25upto 12.75 (C) 85upto11.5 (D) 8.75upto 11.75 (E) 8.75upto 11.25 27. The variable marked with x in the table below is of an unknown value. If the mean of the dataset is 15, what is the value of x? (A) The value of x is 1. (B) The value of x is 3. (C) The value of x is 21. (D) The value of x is 7.5. (E) The value of x is 5. 28. The variable marked with y has the smallest value of the dataset. If the range of the dataset is 23, what is the value of y and what is the mean?

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    (A) The value of y is 11, while the mean is 19. (B) The value of y is 57, while the mean is 28.2. (C) The value of y is 23, while the mean is 21.4. (D) The value of y is 26, while the mean is 22. (E) The value of y is 29, while the mean is 22.75. 29. Ina normally distributed dataset with a mean of 13 and a standard deviation of 2, if the data are standardized by subtracting the mean and dividing by the standard deviation, which of the statements best describes the resulting distribution? (A) Normal with a mean of 13 and a standard deviation of 2 (B) Normal with a mean of 0 and a standard deviation of 2 (C) Normal with a mean of 0 and a standard deviation of 1 (D) Normal with a mean of 6.5 and a standard deviation of 2 (E) Normal with a mean of 6.5 and a standard deviation of 1 30. What measure of center is most resistant to extreme values? (A) Standard deviation (B) Interquartile range (C) Mean (D) Median (E) Range 31. Using this dataset, calculate the mean and the standard deviation. {3,8,10,3,12, 7,10} (A) Mean is 7.5; standard deviation is 3.5 (B) Mean is 7.6; standard deviation is 3.5 (C) Mean is 7.6; standard deviation is 12.3 (D) Mean is 7.6; standard deviation is 4.0 (E) Mean is 8.0; standard deviation is 4.0 32. Which of the statements is true about the standard deviation?

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    (A) Itis typically reported with the median. (B) It cannot be calculated without the correlation coefficient. (C) Itis commonly used to predict future values of variables. (D) Itis calculated by deducting the minimum value from the maximum. (E) It measures the spread of the dataset. 33. Find the five-number summary from the box plot and calculate the interquartile range. (A) Min: 4; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 8 (B) Min: 3; Q1: 5.75; Med: 10.5; Q3: 13.75; Max: 16; IQR: 8 (C) Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 15; IQR: 8 (D) Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 8 (E) Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 9

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    34. Which statement is true of the dataset summarized by this five-number summary? (A) There are no outliers. (B) 3is a mild outlier and 20 is an extreme outlier. (C) 3 and 20 are mild outliers. (D) 20 is an extreme outlier. (E) 20 is a mild outlier. There are no extreme outliers. 35. Which of the statements is true about outliers? (A) They will always occur when an experiment has a dependent variable. (B) Introducing an instrumental variable will certainly create outliers. (C) They should be investigated, as they may indicate an error in the data collection process. (D) They should be ignored and removed from the dataset, as they are a result of a spurious regression. (E) Outliers occur in every dataset and are not a cause for concern. 36. Joan’s test grade was 84. The class average was 72, and the standard deviation was 4.5. What statement best describes her z-score and her test grade? (A) z=-2.67. Compared to the rest of the class, Joan’s grade is low. (B) z=-1.67. Compared to the rest of the class, Joan’s grade is a little below average. (C) z=2.67. Compared to the rest of the class, Joan’s grade is high. (D) z=2.67. Compared to the rest of the class, Joan’s grade is a little above average. (E) z=1.67. Compared to the rest of the class, Joan’s grade is a little above average. 37. In 2007 Forest Whitaker won the Best Actor Oscar at age 45 for the movie The Last King of Scotland. Helen Mirren won the Best Actress

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    Oscar at age 61 for The Queen. The average age for actors is 42.5 with a standard deviation of 7.6. The average age for actresses is 35 with a standard deviation of 9.7. Find the z-scores for each. What statement best describes the results? (A) Whitaker: z = 0.33; Mirren: z = 2.68. Whitaker’s age was about average, and Mirren’s was well above average. (B) Whitaker: z = 0.33; Mirren: z = —2.68. Whitaker’s age was about average, and Mirren’s was well below average. (C) Whitaker: z = 0.33; Mirren: z = 2.68. Whitaker’s age was about average, and Mirren’s was well above average. (D) Whitaker: z = 2.68; Mirren: z = 0.33. Whitaker’s age was well above average, and Mirren’s was about average. (E) Whitaker: z = 0.33; Mirren: z = 2.68. Whitaker’s age was well above average, and Mirren’s was about average. 38. Ina normal distribution, approximately what percentage of data is within one standard deviation of the mean? (A) 34% (B) 68% (C) 64% (D) 32% (E) 65% 39. The range of a dataset is 20 and x has the highest value of the variables provided. What is the value of y and the standard deviation of the dataset if rounded to two decimals? (A) The value of y is 32, and the standard deviation is 7. (B) The value of y is 30, and the standard deviation is 6.41. (C) The value of y is 35, and the standard deviation is 7.92. (D) The value of y is 20, and the standard deviation is 4.03. (E) The value of y is 2, and the standard deviation is 5.76. 40. The distribution of 5,250 standardized test scores is normal with a

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    mean of 258 and a standard deviation of 10. Approximately how many scores are between 248 and 278? (A) 709 (B) 1,785 (©) 3,570 (D) 4,279 (E) 4,988 41. For the probability density curve below, which of the following statements is true? I. The area is exactly 1 underneath it. II. It does not model the distribution of the data. III. It is a function that is always positive. (A) Ionly (B) Iand III only (C) II and III only (D) II only (E) II only

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    42. Why is the following not an example of a valid probability density curve? (A) Because the curve does not follow a normal distribution (B) Because such a function is by definition either constantly positive or negative (C) Because such a function has to have at least two maximum values and one minimum value (D) Because the function cannot be negative (E) Because the function cannot be positive 43. Which of the following is a symmetric probability density curve?

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    IL II. IIL.

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    (A) Ionly (B) Iand III only (C) II and III only (D) II only (E) III only 44. The following box plot illustrates the movement of two variables, Al and B1. Which of the following assumptions is correct? (A) A1 has smaller outliers compared to B1. (B) The value of the median is higher for B1. (C) The range of the data is larger in Al. (D) The two variables have medians of the same value. (E) A1 has problems with outliers that are larger compared to most of the dataset, while B1 has outliers that are smaller than most of the dataset. 45. Choose the five-number summary that matches this stem plot.

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    (A) Min: 13; Q1: 22.5; Med: 27; Q3: 33.5; Max: 51 (B) Min: 13; Q1: 23; Med: 26; Q3: 34; Max: 51 (C) Min: 13; Q1: 22.5; Med: 26; Q3: 33.5; Max: 51 (D) Min: 13; Q1: 23; Med: 27; Q3: 33.5; Max: 51 (E) Min: 13; Q1: 23; Med: 27; Q3: 34; Max: 51 46. The histograms below show the number of cat and dog owners based on the number of each animal owned. Choose the best description from the statements below. (A) There are more cat owners than dog owners. There are more cats than dogs. (B) There are more cat owners than dog owners. There are more dogs than cats.

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    (C) There are more dog owners than cat owners. There are more cats than dogs. (D) There are more dog owners than cat owners. There are more dogs than cats. (E) The cat owners are equal to dog owners. There are more cats than dogs. 47. The dataset of water consumption for a small town in gallons per day is listed. What is the effect on the mean and standard deviation if consumption is increased by 50 gallons per day? {166, 179, 193, 175, 144, 151, 173, 175, 177, 160, 195, 225, 240, 144, 162, 145, 177, 163, 149, 188} (A) The mean and standard deviation remain the same. (B) The mean remains the same. The standard deviation increases by (C) The mean increases by 50. The standard deviation remains the same. (D) The mean and standard deviation increase by 50. (E) The mean increases by 50. The standard deviation increases by 48. A random sample of households and the number of cars per household are shown in the bar chart. What is the best estimate of the sample mean?

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