The clarity and cut of a diamond are two of the four C€™s of diamond grading. (The other two are color and carat.) For a sample of diamonds, the following table lists the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS, slightly included, SI and included, I) for the two lowest ratings for cut, which are €œgood€ and €œfair.€ The data for this exercise are in the Diamonds file on the book€™s website.

a. Find the conditional proportions for the five categories of clarity, given cut.
b. Sketch (or create using software) a side-by-side (or stacked) bar graph that compares the two cuts on clarity. Summarize findings in a paragraph.
c. Based on these data, is there an association between the cuts and clarity? Explain.

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Clarity by Cut Clarity SI Total Cut IF VVS Vs Good Fair 55 4 3 3 16 80 44 30