Diamonds sold at retail. Refer to the Journal of Statistics Education study of 308 diamonds for sale on the open market, Exercise 2.157 (p. 144). Recall that the file contains information on the quantitative variables, size (number of carats) and price (in dollars), and on the qualitative variables, color (D, E, F, G, H, and 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.
a. Set up the null and alternative hypotheses for determining whether the means of the quantitative variable differ for the levels of the qualitative variable.
b. Use the data to conduct the test, part a, at a = 10. State the conclusion in the words of the problem.
c. Check any assumptions required for the methodology used in part b to be valid.
d. Follow up the analysis with multiple comparisons of the treatment means. Use an experimentwise error rate of .05. Interpret the results practically.
U.S. wine export markets. The Center for International Trade Development (CITD), provides a listing of the top 30 U.S. export markets for sparkling wines. Data on the amount exported (thousands of dollars) and 3-year percentage change for the 30 countries in a recent year are saved in the WINEX file. (Data for 5 countries are listed in the table.) Descriptive statistics for these variables are shown in the Minitab printout (next column).
a. Locate the mean amount exported on the printout and practically interpret its value.
b. Locate the median amount exported on the printout and practically interpret its value.
c. Locate the mean 3-year percentage change on the printout and practically interpret its value.
d. Locate the median 3-year percentage change on the printout and practically interpret its value.
e. Use the information on the printout to find the range of the amount exported.
f. Locate the standard deviation of the amount exported on the printout.
g. Use the result, part f, to find the variance of the amount exported.
h. If one of the top 30 countries is selected at random, give an interval that is likely to include the export amount for this country.