Chapter 2 Homework Solutions - Chapter 2 Solutions 2.1 The...

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Chapter 2 Solutions2.1.The cases are students.2.2.When students are classified like this, PSQI is being used as a categorical variable,because each student is categorized by the group he/she falls in.One advantage is that it might simplify the analysis, or at least it might simplify theprocess of describing the results. (Saying that someone fell into the “poor” category is easierto interpret than saying that person had a PSQI score of 12.) A more subtle issue is that it isnot clear whether finding an average is appropriate for these numbers; technically, averagesare not appropriate for a quantitative measurement unless the variable is measured on an“interval” scale, meaning (for example) that the difference between PSQI scores of 1 and 2is the same as the difference between PSQI scores of 10 and 11.2.3.With this change, the cases are cups of Mocha Frappuccino (as before). The variables(both quantitative) are size and price.2.4.One could make the argument that being subjected to stress makes it more difficult tosleep, so that SUDS (stress level) is explanatory and PSQI (sleep quality) is the response.2.5. (a)The spreadsheet should look like theimage on the right (especially if studentsuse the data file from the companion CD).(b)There are 10 cases.(c)The image on theright shows the column headings used on thecompanion CD; some students may createtheir own spreadsheets and use slightly dif-ferent headings. (The values of the variablesshould be the same.)(d)The variables inthe second and third columns (“Bots” and“SpamsPerDay”) are quantitative.2.6.Stemplots are shown; histograms would be equivalent. Studentsmay choose different ways to summarize the data, such as bargraphs (one bar for each botnet). Note that summarizing eachvariable separately does not reveal therelationshipbetween thetwo variables; that is done using a scatterplot in the next exercise.Because both distributions are skewed, we prefer five-numbersummaries to the mean and standard deviation.xsMinQ1MQ3MaxBots (thousands)99.796.6122067.5150315Spams/day (billions)13.618.60.3527.01660Bots01223058121582231Spams/day0002359106230456088
Solutions892.7. (a)The scatterplot is on the right.(b)Bobax is the second point from the right.(Bobax has the second-highest bot count with185 thousand, but is relatively low in spammessages at 9 billion per day.)0102030405060050100150200250300350Spams per day (billions)Bots (thousands)Bobax2.8. (a)The resulting spreadsheet isnot shown.(b)Scatterplot on theright.(c)The points are arrangedexactly as before, but the largenumbers on the axes are distracting.010,000,000,00020,000,000,00030,000,000,00040,000,000,00050,000,000,00060,000,000,0000100,000200,000300,000Spams per dayBots2.9.Size seems to be the most reasonablechoice for explanatory variable because itseems nearly certain that Starbucks first de-cided which sizes to offer, then determinedthe appropriate price for each size (ratherthan vice versa). The scatterplot shows apositive association between size and price.

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