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:

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A legal term describing a condition that must be fulfilled before a contract or agreement becomes effective or before a party is obligated to perform.

Harvard Medical School

A globally prestigious medical school located in Boston, Massachusetts, known for its research, teaching, and clinical care.

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Something that appears real or possible but is neither, often due to being deceptive or misleading.