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

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GUIDE FORSTUDENTACTIVITYWORKBOOKSULLIVANSTATISTICSSERIESSIXTHEDITIONMichael Sullivan, IIIJoliet Junior College

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iTable of ContentsActivity Title (section number)Page NumberChapter 1:Building a Survey in StatCrunch2Introducing Statistics Through Quotes (1.1)3Categorizing Student Survey Data (1.1)4Comparing Sampling Methods (1.4)5Designing an Experiment (1.6)6Chapter 2:Exploring Histograms with StatCrunch (2.2)9Sorting Histograms by Shape (2.2)10Predicting Distribution Shape (2.2)11Constructing and Comparing Graphical Representations (2.2-2.3)12Recognizing and Correcting Misleading Graphs (2.4)13Chapter 3:Understanding Measures of Center (3.1)15Comparing Statistics to Parameters (3.1-3.2)16Exploring Standard Deviation (3.2)17Understanding the Standard Deviation Formula (3.2)18Scaling and Shifting Data (3.4)20Matching Boxplots and Histograms (3.5)21Chapter 4:Exploring Properties of the Linear Correlation Coefficient (4.1)23Finding a Least-Squares Regression Line (4.2)24Examining the Relationship Between Arm Length and Height (4.2)25Minimizing the Sum of the Squared Residuals (4.2)27What Does It Mean to “Regress to the Mean”? (4.2)28Understanding Influential Observations (4.3)31Investigating the Coefficient of Determination (4.3)32Chapter 5:Demonstrating the Law of Large Numbers (5.1)35Finding the Probability of Getting Heads (5.1)36Interpreting Conditional Probabilities (5.4)37Let’s Make a Deal (5.4)38Calculating the Probability of Winning the Lottery (5.5)39Exploring the Duplicate Birthday Problem (5.6)40Tennis Anyone? (5.6)41

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

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

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ivThe subject of statistics, like many things in life, is best learned throughactive participation. Your students will better understand statisticalconcepts and be more able to apply them if they are actively engagedduring class. These activities give you numerous options for teaching,reinforcing, and applying statistical understanding throughout a typicalfirst course in statistics.Teaching statistics presents the familiar challenge of covering too muchcontent in too little time. It is often difficult to find time to do activitieswith a statistics class and still teach all the material you need to teach.Consider ways that you can incorporate activities into your currentapproach to teaching statistics without necessarily using more time.Perhaps you can start an activity in class and have students complete it ontheir own. Perhaps you can replace a lecture with an activity that teachesthe same concepts. Perhaps you can do an activity as a demonstration toreduce the time commitment. The activities are designed to be flexibleand support a variety of classroom uses.If you are doing activities that utilize applets, either go towww.statcrunch.com, or www.pearsonhighered.com/sullivanstats toaccess the applet.

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1Chapter 1Data Collection

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2Building a Survey Using StatCrunch1.Write survey questions that allow you to answer a research question. The survey should includedemographic information (gender, age, political affiliation, and so on). The survey should also includequestions that you wish to have answered. For ideas on the types of questions you might ask, consultthe local newspaper, polling organizations (such as Harris Interactive, Pew Research, and Gallup) forquestions that they have asked. This will allow you to compare the results of your survey (andsubgroups of individuals within your survey) to the polling organizations. It is important that yoursurvey 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 athttps://youtu.be/hf4ZTLMX5D8.3.Build your survey in StatCrunch and administer it. You should attempt to secure at least 200 responsesto your survey, so be sure to utilize social media outlets (Facebook and Twitter) along with other formsof electronic communication (websites and e-mail) to spread the word about your survey. Ask theindividuals who take your survey to share the link with others. This will help to develop a morerepresentative sample (than just your family and friends).4.Summarize the results of your survey as you develop more skills. For example, when you are inChapter 2, create some nice visualizations of the data. In Chapter 3, determine some summarystatistics. Are there any outliers? What are the explanations, if any, for the outliers? Maybe drawside-by-side boxplots by some qualitative variable (such as gender or political affiliation). In Chapter4, 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 theresults of the survey. Do some estimation of parameters (i.e. confidence intervals). Be sure to verifythe model requirements are satisfied. Compare two segments of the sample (Republicans versusDemocrats; High School Graduates versus College Graduates). The ability to do these types ofcomparisons 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 thecourse of the semester, you will develop a report summarizing the results of your survey.

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3Introducing Statistics Through QuotesNotes:This activity works well on the first day of class since it introduces students to the subject and does not requireany prior knowledge. You can have students work in pairs or groups to fill in the quotes that are familiar tothem first and then use logic and a process of elimination to complete the rest. If students are unable to finish inthe 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 conclusionsor 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 otherstudents can determine who said it.•This can be used as an ice-breaker activity on the first day. You can type the quotes andmissing words individually on slips of paper and have students work the room to find theword that completes their quote.•Students can choose one of these quotes at the end of the semester and write an essay on howit relates to the course.Answers:1.uncertainty2.opinion3.assumptions4.numbers5.measure6.approximate7.languages8.certain9.make10. suggestive11. averages12. statistic13. statistically14. probability15. lottery16. accuracy17. truth18. illumination19. conclusions20. experimentOverview:There are numerous popular quotes about statistics, many of which are already familiar to students. Adiscussion of famous statistical quotes at the beginning of the semester provides a great opportunity toexplain what the subject of statistics is all about and introduce students to some of the terminologyused in the subject.Textbook:Section 1.1Time:10 minutes

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4Categorizing Student Survey DataNotes: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 ofmeasurement and even discrete versus continuous. The data classification will be challenging for them! This isa 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 thatthere are certainly boxes with more than one reasonable answer. After students have completed theclassification chart, you will want to have a whole-class discussion and have students share and defend theirchoices.There are numerous possible uses for this data later in the semester. You might consider loading it intoStatCrunch 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) foreach 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 collegestudents 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 thenumber 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 asan ice-breaker activity, but also provides lots of data for future use in the course.Textbook:Section 1.1Time:10 minutes to collect data, at least 20 minutes to classify data and discuss

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5Comparing Sampling MethodsNotes:You can give students some input in the question used for this activity. Consider having them look on theGallup website for homework and find a recently asked question or do this together as a class. It might beinteresting 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 inthe text. You might consider discussing the different sampling methods the day before this activity orhave the students read them in the book in preparation for this activity.Textbook:Section 1.4Time:50 minutes

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6Designing an ExperimentNotes:This activity presents a huge task for students. Although the steps are outlined in the activity, there are stillmany choices for students to make. You will want to provide enough guidance for the students to be successfulwhile 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 canintroduce the activity and guide students through the first four steps. Then they will need time to make theplanes. 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 aredeveloped. Students could be assigned groups to complete the activity out of class for Chapter 1. Whendescriptive statistics are developed, students could revisit the problem, summarize, and visualize theexperimental results to assist in analyzing them. When inferential statistics are developed, students could returnto 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-bagpaper, or printer paper?Response variable:Length of the flightStep 2:1. Who makes the planes (You may want to fix this at a single level. If you have more than oneindividual making the planes, you will have a randomized block design. We do not care about theimpact the person has on the flight distance, but we do want to eliminate variability attributed to theperson making the planes.)2. Who flies the planes3. Paper choice4. 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 thenumber of students in the class. Alternatively, each student could make 3 planes of each type to havemore 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 anexperiment, even for something simple like paper airplanes.Textbook:Section 1.6Materials:Newspaper, brown-bag paper, 24-pound printer paperPaper airplane designsTime:See note below

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

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8Chapter 2Organizing and Summarizing Data

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9Exploring Histograms with StatCrunchNotes:This activity requires that students have a data set to work with in StatCrunch. If you did the Student DataSurvey in Chapter one and saved the data on StatCrunch, then have the students use the data file for thisactivity. If you did not use the Student Data Activity or do not have the results on StatCrunch, then you canprovide another data set or have students use one that is already available on StatCrunch. If your students havenot used StatCrunch before, it would help if you can provide a demonstration for the class to make it easier forstudents 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 distributionand 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 offour students so that they can compare and discuss their histograms as they make them. Alternatively, youcould assign different variables to different students to reduce students’ ability to get information from eachother 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 limit4a.class widthOverview:Since histograms will be used frequently in the rest of the course, it is important that studentsunderstand how to interpret histograms and what they reveal about the shape of the distribution of adata set. Students also need to realize that the choices they make about class limits and class widthwill affect the look of the histogram and the impression it gives about the data. Since makingmultiple histograms by hand is time consuming, technology provides a convenient and efficient wayto explore these effects.Textbook:Section 2.2Time:25 minutes

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10Sorting Histograms by ShapeNotes: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 willoften come up with creative names that make more sense to them than the formal category names. Let studentsknow that sorting histograms is subjective and not everyone will agree. It is important that they can defendtheir categories and choices, however.Students are likely to have difficulty categorizing graph #8 with the Height data. Some students might describeit as “twin –peaked” or notice the up-down-up pattern. Other students might think it falls into one of the otherexisting categories. Ask students why they think the Height histogram has this shape and see if they considerthat 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 histogramscould be given to a group of students to sort physically.Possible answers:Category NameCategory DescriptionList of Graphs IncludedBell-shapedThe highest frequency occurs in the middle, andthe frequencies fall off to the left and right. Thehistogram is fairly symmetric.IQ Scores (#2)Sum of Two Dice (#9)ACT Scores (#12)UniformThe frequency of each value of the variable isfairly evenly spread out across the values of thevariable.Random Numbers (#1)Die Roll (#4)Skewed RightThe tail to the right of the peak is longer than thetail to the left of the peak.Wait Time (#3)Income ($1000s) (#7)Student Ages (#10)Number of Children (#11)Skewed LeftThe tail to the left of the peak is longer than thetail to the right of the peak.Weight (lbs) (#5)Grades (#6)BimodalThere 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 2.2Time:10 – 15 minutes

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