11.65 Clarity of diamonds Does the clarity of a diamond depend on its cut? Exercise 3.4 showed data, reproduced below, on 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 “good” and “fair.”

a. Verify, using software, that X2 = 0.267 for this table.
The (raw) data are available on the book’s website as Diamonds.csv.

b. Can you use the chi-squared distribution to find a P-value? Why or why not?

c. Of 10,000 random permutations, 9,908 resulted in an X 2 value as large or larger than the one observed.
Find the (approximate) permutation P-value and interpret.

d. Use the Permutation Test of Independence web app accessible from the book’s website to enter the contingency table and replicate the results from part c.

Transcribed Image Text:

Clarity Cut IF VVS vs SI I Total Good 2 4 16 55 3 80 Fair 1 3 8 30 2 44