307 Diamonds Were Sampled and Randomly Sorted into Three Groups

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
$\begin{array}{llcccc}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { CERT } & 2 & 8.3265 & 4.16326 & 83.21 & 0.0000 \\\text { Error } & 305 & 15.2604 & 0.05003 & & \\\text { Total } & 307 & 23.5869 & & &\end{array}$

Specify the null hypothesis for a test to compare the mean size of a diamond for the three certification groups (HRD, GIA, and IGI) .

A) At least two of the population mean carat weights differ for the three certification groups.
B) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { HRD } } = \mu _ { \mathrm { GIA } } = \mu _ { \mathrm { IGI } }$ , where $\mu _ { \mathrm { j } } =$ mean carat weight for certification group i
C) $\mathrm { H } _ { 0 } : \mu = 0$ , where $\mu =$ mean carat weight.
D) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { HRD } } = \mu _ { \mathrm { GIA } } = \mu _ { \mathrm { IGI } } = 0$ , where $\mu _ { \mathrm { j } } =$ mean carat weight for certification group i