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Diamonds sold at retail. Refer to the Journal of
Chapter 9, Problem 103SE(choose chapter or problem)
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. 117). 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 \(\alpha=10\). 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.
Questions & Answers
QUESTION:
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. 117). 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 \(\alpha=10\). 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.
ANSWER:Step 1 of 11
(a) Write the appropriate hypotheses.
Let the mean sizes of the 6 diamonds be denoted as \(\mu_{1}, \mu_{2}, \mu_{3}, \mu_{4}, \mu_{5}\) and \(\mu_{6}\).
Null hypothesis:
\(H_{0}: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}=\mu_{6}\)
That is, there is no significant difference among the mean size of diamonds and 6 colors.
Alternative hypothesis:
\(H_{a}\): At least two treatment means differ.
That is, there is a significant difference among the mean size of diamonds and 6 colors.