Which of the following statements are not true regarding the model $X _ { y } = \mu + \alpha _ { i} + \beta _ { j} + \varepsilon _ { y }$ where $\sum _ { l = 1 } ^ { \prime } \alpha _ { 1 } = 0 \text { and } \sum _ { j = 1 } ^ { j } \beta _ { j } = 0 ?$
A) $\mu$
Is the true grand mean; that is, the mean response averaged over all levels of both factors A and B.
B) $\alpha _ { i }$
Is the effect of Factor A at level i.
C) $\beta _ { j }$
Is the effect of Factor B at level j.
D) $\varepsilon _ { y }$
Are assumed independent and normally distributed with mean 0 and variance 1.
E) All of the above statements are true.

Question

Quizplus · Accepted Answer

The statement in D is not necessarily true as it assumes a specific distribution and variance for $\varepsilon _ { y }$ without specifying that these conditions must always hold. In general, $\varepsilon _ { y }$ are assumed to be independent and normally distributed with mean 0, but the variance does not have to be 1; it can be any positive value $\sigma^2$.

Which of the Following Statements Are Not True Regarding the Model