Given the following observations collected according to the one-way analysis of variance design,

(a) decompose each observation \(y_{i j}\) as

\[y_{i j}=\bar{y}+\left(\bar{y}_{i}-\bar{y}\right)+\left(y_{i j}-\bar{y}_{i}\right)\]

and obtain the sum of squares and degrees of freedom for each component;

(b) construct the analysis of variance table and test the equality of settings using \(\alpha=0.01\).

Transcribed Image Text:

17 15 18 8 6 557 1408 8261 Setting 1 Setting 2 Setting 3 Setting 4 14