307 Diamonds Were Sampled and Randomly Sorted into Three Groups

Multiple Choice

307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI) , that
Certify the appraisal of diamonds. A study was conducted to determine if the average size of
Diamonds reported by these three certification groups differ. A completely randomized design was
Used and the resulting ANOVA table is shown below. One-Way AOV for CARAT by CERT
$\begin{array}{llrcrc}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { CERT } & 2 & 8.3265 & 4.16326 & 83.21 & 0.0000 \\\text { Error } & 305 & 15.2604 & 0.05003 & & \\\text { Total } & 307 & 23.5869 & & &\end{array}$

Give a practical conclusion for the test in the words of the problem. Use $\alpha = 0.10$ to make your conclusion.

A) There is insufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups.
B) There is sufficient evidence to indicate that the mean carat weight for the HRD group equals the mean carat weight for the IGI group.
C) There is sufficient evidence to indicate that the mean carat weight for the GIA group is lower than the other two groups.
D) There is sufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups.