Listed below are measured hardness indices from three different collections of gemstones.
Collection Hardness Indices
A 9.3 9.3 9.3 8.6 8.7 9.3 9.3 -- --- --- --- --- --- 9.91 0.10
B 8.7 7.7 7.7 8.7 8.2 9.0 7.4 7.0 --- --- --- --- --- 8.03 0.60
C 7.2 7.9 6.8 7.4 6.5 6.6 6.7 6.5 6.5 7.1 6.7 5.5 7.3 6.82 0.34
You are also given that x mean = 7.99
Use a 5% significance level (95% confidence level) to test the claim that the different collections have the same mean hardness.