Banknotes of the Swiss franc are issued by the Swiss National Bank in denominations of 10, 20, 50, 100, 200 and 1,000 Swiss francs. Despite extensive efforts to control the physical attributes of these notes, counterfeit (referred to as 'Fake') notes are sometimes produced and used by criminal actors operating in the Swiss retail economy. In this way, the counterfeit notes end up contaminating the pool of authentic (referred to as 'Real") notes that normally circulate throughout the European banking system. A study comparing certain physical attributes of both authentic and counterfeit Swiss banknotes investigated whether a physical measurement, such as the length of a note, differs for Fake and Real banknotes. In total, 200 bank notes, 100 of each type (either Real or Fake) were measured. The data from this study was imported into R and is contained in an tibble named df. The columns of df are Type - binary indicator variable (Type = 1 if note is Fake, Type = 0 if note is Real) . length - length of the note, in millimeters (mm) Histogram and kernel density plots for the two types of banknotes are shown in Figure 1. Real 1.0 Fake density 0.5 0.0 213 214 215 216 217 length of banknote, in mm Figure 1.1: Overlayed histogram and kernel density plots for the length of Real and Fake bank notes in Swiss banknote study. In addition, some commonly used descriptive statistics, calculated for each type of banknote, are shown in Table 1. Type mean sd se median Q1 Q3 IQR min max 0 215 0.375 0.053 215 215 215 0.5 214 216 1 215 0.352 0.035 215 215 215 0.4 214 216