Solve the problem. 307 diamonds were sampled and randomly sorted into three grou

Question

Solve the problem. 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. e-Way AOV for CARAT by CERT ource DF CERT Error Total MS .32654.16326 83.21 305 307 15.26040.05003 235869 Specify the alternative hypothesis for a test to compare the mean size of a diamond for the three certification groups (HRD, GIA, and IG) At least two of the population mean carat weights differ for the three certification groups. Ho:-o, where = HO: RD" GIA" 1GI : O. where mean carat weight. = mean carat weight for certification group i

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: HRD = GIA = IGI

Alternative hypothesis: At-least one of the is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 83.21

The P-value = 0.0000

Interpret results. Since the P-value (0.000) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

Reject H0, There is sufficient evidence for significant differences between the size of diamonds among three organisations.

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