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
Source DF SS MS F P
CERT 2 8.3265 4.16326 83.21 0.0000
Error 305 15.2604 0.05003
Total 307 23.5869
Specify the null hypothesis for a test to compare the mean size of a diamond for the three certification groups (HRD, GIA, and IGI).
◦ H0: μHRD = μGIA = μIGI = 0, where μj = mean carat weight for certification group i
◦ At least two of the population mean carat weights differ for the three certification groups.
◦ H0: μ = 0, where μ = mean carat weight.
◦ H0: μHRD = μGIA = μIGI, where μj = mean carat weight for certification group i
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