307 Diamonds Were Sampled and Randomly Sorted into Three Groups $\text {One-Way AOV for CARAT by CERT}$

question 21

Short Answer

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. $\text {One-Way AOV for CARAT by CERT}$
$\begin{array}{lccccc}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { CERT } & 2 & 8.3265 & 4.16326 & 83.21 & 0.0000 \\\text { Error } & 305 & 15.2604 & 0.05003 & & \\\text { Total } & 307 & 23.5869 & & &\end{array}$

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

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

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Definitions:

Strategic Leadership

The ability of influencing others to voluntarily make decisions that enhance the prospects for the organization's long-term success while maintaining long-term financial stability.

Performance Determinants

Performance determinants are factors that can influence an individual's or organization's ability to achieve objectives, including skills, resources, and external conditions.

Flexible Leadership Theory

A theory suggesting organizations can achieve success through adaptable leadership practices tailored to operational requirements, change, and efficiency.

External Environment

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