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Solution Manual for Statistics: Informed Decisions Using Data, 6th Edition

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    G UIDE FOR S TUDENT A CTIVITY W ORKBOOK S ULLIVAN S TATISTICS S ERIES S IXTH E DITION Michael Sullivan, III Joliet Junior College

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    i Table of Contents Activity Title (section number) Page Number Chapter 1: Building a Survey in StatCrunch 2 Introducing Statistics Through Quotes (1.1) 3 Categorizing Student Survey Data (1.1) 4 Comparing Sampling Methods (1.4) 5 Designing an Experiment (1.6) 6 Chapter 2: Exploring Histograms with StatCrunch (2.2) 9 Sorting Histograms by Shape (2.2) 10 Predicting Distribution Shape (2.2) 11 Constructing and Comparing Graphical Representations (2.2-2.3) 12 Recognizing and Correcting Misleading Graphs (2.4) 13 Chapter 3: Understanding Measures of Center (3.1) 15 Comparing Statistics to Parameters (3.1-3.2) 16 Exploring Standard Deviation (3.2) 17 Understanding the Standard Deviation Formula (3.2) 18 Scaling and Shifting Data (3.4) 20 Matching Boxplots and Histograms (3.5) 21 Chapter 4: Exploring Properties of the Linear Correlation Coefficient (4.1) 23 Finding a Least-Squares Regression Line (4.2) 24 Examining the Relationship Between Arm Length and Height (4.2) 25 Minimizing the Sum of the Squared Residuals (4.2) 27 What Does It Mean to “Regress to the Mean”? (4.2) 28 Understanding Influential Observations (4.3) 31 Investigating the Coefficient of Determination (4.3) 32 Chapter 5: Demonstrating the Law of Large Numbers (5.1) 35 Finding the Probability of Getting Heads (5.1) 36 Interpreting Conditional Probabilities (5.4) 37 Let’s Make a Deal (5.4) 38 Calculating the Probability of Winning the Lottery (5.5) 39 Exploring the Duplicate Birthday Problem (5.6) 40 Tennis Anyone? (5.6) 41

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    ii Chapter 6: Finding the Expected Value of a Game (6.1) 43 Exploring a Binomial Distribution from Multiple Perspectives (6.2) 44 Using Binomial Probabilities in Baseball (6.2) 45 Designing a Game (6.2) 46 Chapter 7: Constructing Probability Distributions Involving Dice (7.1) 48 Fooled by Randomness (7.1) 50 Home Run Distances (7.2) 51 Grading on a Curve (7.2) 53 Modeling with the Normal Distribution (7.2) 55 Analyzing Standardized Test Scores (7.2) 56 Playing Plinko (7.4) 57 Chapter 8: Creating a Sampling Distribution for the Mean (8.1) 59 Analyzing the Variability in Sample Means (8.1) 60 Describing the Distribution of the Sample Mean: Approximately Normal Population (8.1) 61 Simulating IQ Scores (8.1) 63 Sampling from Normal and Non-Normal Populations (8.1) 64 Describing the Distribution of the Sample Mean: Non-Normal Data (8.1) 65 Creating a Sampling Distribution for a Proportion (8.2) 67 Describing the Distribution of the Sample Proportion (8.2) 68 Describing the Distribution of the Sample Proportion Using the Urn Applet (8.2) 69 Chapter 9: Exploring the Effects of Confidence Level, Sample Size, and Shape I (9.1) 72 Constructing a Confidence Interval with M&M’s (9.1) 73 Constructing a Confidence Interval for Average Temperature (9.2) 74 Exploring the Effects of Confidence Level, Sample Size, and Shape II (9.2) 75 Constructing a Confidence Interval from a Non-Normal Distribution (9.2) 76 Constructing a Confidence Interval for Die Rolls (9.2) 77 The Role of Sample Size in the Construction of Confidence Intervals (9.2) 78 Take Me Out to the Ball Game (9.2) 80 Finding a Bootstrap Confidence Interval (9.5) 81 Chapter 10: The Logic of Hypothesis Testing (10.1) 83 Sensitivity and Specificity (10.1) 84 Interpreting P -Values (10.2) 86 Testing a Claim with Skittles I (10.2) 87 Understanding Type I Error Rates I (10.2) 88 Testing Cola Preferences (10.2) 89

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    iii Testing a Claim with Beads (10.2) 90 Analyzing a Research Article I (10.2) 91 Testing a Claim with Skittles II (10.3) 92 Understanding Type I Error Rates II (10.3) 93 Using Bootstrapping to Test a Claim (10.5) 94 Computing the Power of a Test (10.6) 97 Chapter 11: Making an Inference about Two Proportions (11.1) 99 Analyzing Rates of Drug Side Effects (11.1) 100 Predicting Basketball Game Outcomes (11.1) 101 Considering the Effects of Grammar (11.1) 103 Analyzing Kissing Data (11.1) 104 Analyzing a Research Article II (11.2) 106 Comparing Arm Span and Height (11.2) 107 Comparing Rental Car Prices (11.2) 108 Using Randomization Test for Independent Means (11.3) 109 Comparing Bull and Bear Markets (11.3) 111 Differentiating Between Practical and Statistical Significance (11.3) 113 Chapter 12: Performing a Goodness-of-Fit Test (12.1) 115 Testing for Homogeneity of Proportions (12.2) 116 Chapter 13: Designing a Randomized Complete Block Design (13.3) 119 Performing a Two-Way ANOVA (13.4) 120 Chapter 14: Testing the Significance of a Regression Model (14.1) 112 Using a Randomization Test for Correlation (14.1) 123

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    iv The subject of statistics, like many things in life, is best learned through active participation. Your students will better understand statistical concepts and be more able to apply them if they are actively engaged during class. These activities give you numerous options for teaching, reinforcing, and applying statistical understanding throughout a typical first course in statistics. Teaching statistics presents the familiar challenge of covering too much content in too little time. It is often difficult to find time to do activities with a statistics class and still teach all the material you need to teach. Consider ways that you can incorporate activities into your current approach to teaching statistics without necessarily using more time. Perhaps you can start an activity in class and have students complete it on their own. Perhaps you can replace a lecture with an activity that teaches the same concepts. Perhaps you can do an activity as a demonstration to reduce the time commitment. The activities are designed to be flexible and support a variety of classroom uses. If you are doing activities that utilize applets, either go to www.statcrunch.com, or www.pearsonhighered.com/sullivanstats to access the applet.

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    1 Chapter 1 Data Collection

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    2 Building a Survey Using StatCrunch 1. Write survey questions that allow you to answer a research question. The survey should include demographic information (gender, age, political affiliation, and so on). The survey should also include questions that you wish to have answered. For ideas on the types of questions you might ask, consult the local newspaper, polling organizations (such as Harris Interactive, Pew Research, and Gallup) for questions that they have asked. This will allow you to compare the results of your survey (and subgroups of individuals within your survey) to the polling organizations. It is important that your survey include both quantitative and qualitative data. Have fun with the types of questions you ask. This is your survey and your project, so be creative. 2. Watch the video “StatCrunch Survey” available at www.sullystats.com/statistics-videos or at https://youtu.be/hf4ZTLMX5D8. 3. Build your survey in StatCrunch and administer it. You should attempt to secure at least 200 responses to your survey, so be sure to utilize social media outlets (Facebook and Twitter) along with other forms of electronic communication (websites and e-mail) to spread the word about your survey. Ask the individuals who take your survey to share the link with others. This will help to develop a more representative sample (than just your family and friends). 4. Summarize the results of your survey as you develop more skills. For example, when you are in Chapter 2, create some nice visualizations of the data. In Chapter 3, determine some summary statistics. Are there any outliers? What are the explanations, if any, for the outliers? Maybe draw side-by-side boxplots by some qualitative variable (such as gender or political affiliation). In Chapter 4, determine if there are any associations between quantitative variables. Qualitative variables? 5. Once you get into Part IV of the text—inferential statistics—conduct some inference based on the results of the survey. Do some estimation of parameters (i.e. confidence intervals). Be sure to verify the model requirements are satisfied. Compare two segments of the sample (Republicans versus Democrats; High School Graduates versus College Graduates). The ability to do these types of comparisons hinges on the type of demographic information you collected in the original survey. So, be sure your survey has this type of data in it. 6. State any final conclusions you have found based on your survey results and data analysis. In this activity, you will build a survey using StatCrunch. As you progress through topics during the course of the semester, you will develop a report summarizing the results of your survey.

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    3 Introducing Statistics Through Quotes Notes: This activity works well on the first day of class since it introduces students to the subject and does not require any prior knowledge. You can have students work in pairs or groups to fill in the quotes that are familiar to them first and then use logic and a process of elimination to complete the rest. If students are unable to finish in the time you would like to allot in class, they can be encouraged to Google the ones they have not finished. At some point in this activity, refer your students to the definition of statistics (section 1.1): “Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.” There are numerous possible extensions and variations to this activity. Here are a few possibilities: • Students can be asked to find a statistical quote that was not included in this activity. • If you have an online discussion board for your course, students can post a quote and other students can determine who said it. • This can be used as an ice-breaker activity on the first day. You can type the quotes and missing words individually on slips of paper and have students work the room to find the word that completes their quote. • Students can choose one of these quotes at the end of the semester and write an essay on how it relates to the course. Answers: 1. uncertainty 2. opinion 3. assumptions 4. numbers 5. measure 6. approximate 7. languages 8. certain 9. make 10. suggestive 11. averages 12. statistic 13. statistically 14. probability 15. lottery 16. accuracy 17. truth 18. illumination 19. conclusions 20. experiment Overview: There are numerous popular quotes about statistics, many of which are already familiar to students. A discussion of famous statistical quotes at the beginning of the semester provides a great opportunity to explain what the subject of statistics is all about and introduce students to some of the terminology used in the subject. Textbook : Section 1.1 Time : 10 minutes

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    4 Categorizing Student Survey Data Notes: Give students a time limit for collecting the data before they begin so they will be focused. Tell students that classifying the data is not black and white and to expect some disagreement over levels of measurement and even discrete versus continuous. The data classification will be challenging for them! This is a great time to discuss the fact that statistics is subjective and they should not expect the answers to be as well- defined as they were in algebra. Encourage them to justify their choices in the chart and let them know that there are certainly boxes with more than one reasonable answer. After students have completed the classification chart, you will want to have a whole-class discussion and have students share and defend their choices. There are numerous possible uses for this data later in the semester. You might consider loading it into StatCrunch so your students have access to the data later. Possible uses for the data later in the semester: • Ask students to represent one of the variables with several different types of graphs. • Ask students to choose the most appropriate type of graphical display (in their opinion) for each variable. • Ask students to describe the center and spread of one particular variable. • Treat the data as a simple random sample and have students test a claim such as college students get an average of 8 hours of sleep per night. • Treat the data as a simple random sample and have students find a confidence interval for the number of hours of TV college students typically watch each night. Overview: This activity gives students an opportunity to apply the terminology from Section 1.1. It works well as an ice-breaker activity, but also provides lots of data for future use in the course. Textbook : Section 1.1 Time : 10 minutes to collect data, at least 20 minutes to classify data and discuss

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    5 Comparing Sampling Methods Notes: You can give students some input in the question used for this activity. Consider having them look on the Gallup website for homework and find a recently asked question or do this together as a class. It might be interesting for them to compare their class results to the results posted on the Gallup website. A random number generator will be needed for this activity. Overview: This activity gives students a chance to implement some of the sampling methods from section 1.4 in the text. You might consider discussing the different sampling methods the day before this activity or have the students read them in the book in preparation for this activity. Textbook : Section 1.4 Time : 50 minutes

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    6 Designing an Experiment Notes: This activity presents a huge task for students. Although the steps are outlined in the activity, there are still many choices for students to make. You will want to provide enough guidance for the students to be successful while still allowing them to struggle with the enormity of the task and the number of decisions to be made. You will need to allow parts of several different class periods for this activity. In the first period, you can introduce the activity and guide students through the first four steps. Then they will need time to make the planes. Another period might be used to discuss Step 5 before carrying out the experiment in a third period. This activity could be used as a semester-long project that is revisited and extended as additional techniques are developed. Students could be assigned groups to complete the activity out of class for Chapter 1. When descriptive statistics are developed, students could revisit the problem, summarize, and visualize the experimental results to assist in analyzing them. When inferential statistics are developed, students could return to the problem and test the difference between the results. Answers: Step 1: Research question: Will the paper airplanes fly farthest if they are made of newspaper, brown-bag paper, or printer paper? Response variable: Length of the flight Step 2: 1. Who makes the planes (You may want to fix this at a single level. If you have more than one individual making the planes, you will have a randomized block design. We do not care about the impact the person has on the flight distance, but we do want to eliminate variability attributed to the person making the planes.) 2. Who flies the planes 3. Paper choice 4. Wind (fixed by doing experiment inside) Step 3: Each student could make one from each type of paper, resulting in 3 times as many planes as the number of students in the class. Alternatively, each student could make 3 planes of each type to have more replication. Overview: The purpose of this activity is to allow students to see why good experiments need control, randomization, and replication. In addition, students recognize how much thought needs to go into an experiment, even for something simple like paper airplanes. Textbook : Section 1.6 Materials : Newspaper, brown-bag paper, 24-pound printer paper Paper airplane designs Time : See note below

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    7 Step 4: Answers will vary. Step 5: Answers will vary. Students should consider randomization in this part of the experiment. For example, if the students always fly the printer-paper plane first, the results may be misleading due to the “learning curve” in flying the planes. Step 6: Answers will vary.

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    8 Chapter 2 Organizing and Summarizing Data

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    9 Exploring Histograms with StatCrunch Notes: This activity requires that students have a data set to work with in StatCrunch. If you did the Student Data Survey in Chapter one and saved the data on StatCrunch, then have the students use the data file for this activity. If you did not use the Student Data Activity or do not have the results on StatCrunch, then you can provide another data set or have students use one that is already available on StatCrunch. If your students have not used StatCrunch before, it would help if you can provide a demonstration for the class to make it easier for students to find the data set and the applet needed for this activity. This activity should be done after you have taught students how to organize data into a frequency distribution and have at least introduced histograms in Section 2.2. If you want to use this activity as a group assignment, you could assign a particular variable to each group of four students so that they can compare and discuss their histograms as they make them. Alternatively, you could assign different variables to different students to reduce students’ ability to get information from each other and ensure they are each doing their own work. After students have completed this activity, have a discussion to make sure they realize that there is no single “correct” histogram, but there are some histograms that do a very poor job of representing a given variable. Answers: 3a. lower class limit 4a. class width Overview: Since histograms will be used frequently in the rest of the course, it is important that students understand how to interpret histograms and what they reveal about the shape of the distribution of a data set. Students also need to realize that the choices they make about class limits and class width will affect the look of the histogram and the impression it gives about the data. Since making multiple histograms by hand is time consuming, technology provides a convenient and efficient way to explore these effects. Textbook : Section 2.2 Time : 25 minutes

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    10 Sorting Histograms by Shape Notes: This activity is best done with students working in pairs or groups so they can discuss the shapes of the graphs. Encourage students to create categories other than the ones suggested if they think it is warranted. Students will often come up with creative names that make more sense to them than the formal category names. Let students know that sorting histograms is subjective and not everyone will agree. It is important that they can defend their categories and choices, however. Students are likely to have difficulty categorizing graph #8 with the Height data. Some students might describe it as “twin –peaked” or notice the up-down-up pattern. Other students might think it falls into one of the other existing categories. Ask students why they think the Height histogram has this shape and see if they consider that there is a peak for the most common male height and another for the most common female height. You might consider copying the histograms and cutting them apart so that a stack of individual histograms could be given to a group of students to sort physically. Possible answers: Category Name Category Description List of Graphs Included Bell-shaped The highest frequency occurs in the middle, and the frequencies fall off to the left and right. The histogram is fairly symmetric. IQ Scores (#2) Sum of Two Dice (#9) ACT Scores (#12) Uniform The frequency of each value of the variable is fairly evenly spread out across the values of the variable. Random Numbers (#1) Die Roll (#4) Skewed Right The tail to the right of the peak is longer than the tail to the left of the peak. Wait Time (#3) Income ($1000s) (#7) Student Ages (#10) Number of Children (#11) Skewed Left The tail to the left of the peak is longer than the tail to the right of the peak. Weight (lbs) (#5) Grades (#6) Bimodal There are two different peaks in the frequencies. Height (in.) (#8) Overview: In this activity, students will sort 12 histograms into categories based on their shapes. Textbook : Section 2.2 Time : 10 – 15 minutes

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