Emerald Diamonds These data are a subset of the diamonds used in Chapter 19. This data table of 144 diamonds includes the price (in dollars), the weight (in carats), and the clarity grade of the diamonds. The diamonds have clarity grade either VS1 or VVS1. VVS1 diamonds are nearly flawless; VS1 diamonds have more visible (but still small) flaws.
(a) Would it be appropriate to use a two-sample t-test to compare the average prices of VS1 and VVS1 diamonds, or is this relationship confounded by the weights of the diamonds?
(b) Perform the two-sample t-test to compare the prices of the two grades of diamonds. Summarize this analysis as if there are no lurking variables. Do you get the sort of difference that would be expected from the definitions of the categories?
(c) Compare the prices of the two types of diamonds using an analysis of covariance. Summarize the comparison of prices based on this analysis. Use a dummy variable coded as 1 for VVS1 diamonds and 0 otherwise. (Assume for the moment that the model meets the conditions for the MRM.)
(d) Compare the results from parts (b) and (c). What can you conclude about the cost of diamonds of these two grades? You should take into account the precision of the estimates and your answer to part (a).
(e) What problem bedevils the multiple regression used for the analysis of covariance that is not present in the two-sample t-test?