Question: Diamonds sold at retail. Refer to the Journal of Statistics NW Education study of 308 diamonds for sale on the open market, Exercise 2.25 (p. 50). Recall that the DIAMONDS file contains information on the quantitative variables, size (number of carats) and price (in dollars), and on the qualitative variables, color \((\mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H}\), and \(\mathrm{I})\), clarity (IF, VS1, VS2, VVS1, and VVS2), and independent certification group (GIA,HRD, or IGI). Select one of the quantitative variables and one of the qualitative variables.

1. Set up the null and alternative hypotheses for determining whether the means of the quantitative variable differ for the levels of the qualitative variable.
2. Use the data in the DIAMONDS file to conduct the test, part a, at \(\alpha=10\). State the conclusion in the words of the problem.
3. Check any assumptions required for the methodology used in part b to be valid.

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