Three alternatives are suggested for electroplating to reduce dissolved metal cations so that they form a coherent metal coating on an electrode. In an experiment conducted to compare the manufacturing yields using the three alternatives, experimenters record the number of electrodes coated before the metal cations are exhausted. Suppose the data are

Without using the alternative formulas, calculate \[\begin{gathered} \sum_{i=1}^{k} \sum_{j=1}^{n_{i}}\left(y_{i j}-\bar{y}\right)^{2} \sum_{i=1}^{k} \sum_{j=1}^{n_{i}}\left(y_{i j}-\bar{y}_{i}\right)^{2} \\ \text { and } \sum_{i=1}^{k} n_{i}\left(\bar{y}_{i}-\bar{y}\right)^{2} \end{gathered}\]
and verify the identity of Theorem 12.1.

Data From Theorem 12.1

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Alternative X Alternative Y Alternative Z 321 327 319 325 324 331 318 326 328 330 329 322