Eight machines in an experiment under standard conditions, produced quantities$\displaystyle x_{1},x_{2},,,,,x_{8}$ of their product. When the experiment was repeated, under the same conditions except for the use of a different lubricant, the machines produced$\displaystyle y_{1},y_{2},,,,y_{8}$. If $\displaystyle \sum(x_{r})=8.73$ $\displaystyle \sum(y_{r})=9.21$ and $\displaystyle \sum(y_{r}-x_{r})^2=0.051$ is there evidence that the lubricant has improved productivity? Explain the assumptions made in the analysis. the sums are from the subscripts 1 to 8. Does anyone have any idea how to derivate the test stat 3.01 given in the answers? Presumably the varience is known but im having some difficulty getting it, thanks ok i think you use normal and treat the differance somehow as one sample, still cant get s.d