A two-factor experiment where factor A consists of I levels, factor B consists of J levels, and there is only one observation on each of the IJ treatments, can be represented by the model $X _ { 4 } = \mu + \alpha _ { i } + \beta _ { j } + \varepsilon _ { y } \text { where } \sum _ { i = 1 } ^ { j} \alpha _ { i } = 0 \text { and } \sum _ { j = 1 } ^ { j } \beta _ { j } = 0$ . Which of the following is the correct form in testing the null hypothesis that the different levels of factor A have no effect on true average response?
A) : $\alpha _ { 1 } = \alpha _ { 2 } = \ldots \ldots = \alpha _ { j } = 0$
B) $ : \beta _ { 1 } = \beta _ { 1 } = \ldots \ldots = \beta _ { 3 } = 0$
C) $ \text { : at least one } \alpha _ { i } \neq 0$
D) $ \text { : at least one } \beta _ { \mathrm { j } } \neq 0$
E) None of the above answers are correct.

Question

A two-factor experiment where factor A consists of I levels, factor B consists of J levels, and there is only one observation on each of the IJ treatments, can be represented by the model $X _ { 4 } = \mu + \alpha _ { i } + \beta _ { j } + \varepsilon _ { y } \text { where } \sum _ { i = 1 } ^ { j} \alpha _ { i } = 0 \text { and } \sum _ { j = 1 } ^ { j } \beta _ { j } = 0$ . Which of the following is the correct form in testing the null hypothesis that the different levels of factor A have no effect on true average response?
A) : $\alpha _ { 1 } = \alpha _ { 2 } = \ldots \ldots = \alpha _ { j } = 0$ 
B) $ : \beta _ { 1 } = \beta _ { 1 } = \ldots \ldots = \beta _ { 3 } = 0$ 
C) $ \text { : at least one } \alpha _ { i } \neq 0$ 
D) $ \text { : at least one } \beta _ { \mathrm { j } } \neq 0$ 
E) None of the above answers are correct.

Quizplus · Accepted Answer

The Answer of A two-factor experiment where factor A consists of I levels, factor B consists of J levels, and there is only one observation on each of the IJ treatments, can be represented by the model $X _ { 4 } = \mu + \alpha _ { i } + \beta _ { j } + \varepsilon _ { y } \text { where } \sum _ { i = 1 } ^ { j} \alpha _ { i } = 0 \text { and } \sum _ { j = 1 } ^ { j } \beta _ { j } = 0$ . Which of the following is the correct form in testing the null hypothesis that the different levels of factor A have no effect on true average response?
A) : $\alpha _ { 1 } = \alpha _ { 2 } = \ldots \ldots = \alpha _ { j } = 0$ 
B) $ : \beta _ { 1 } = \beta _ { 1 } = \ldots \ldots = \beta _ { 3 } = 0$ 
C) $ \text { : at least one } \alpha _ { i } \neq 0$ 
D) $ \text { : at least one } \beta _ { \mathrm { j } } \neq 0$ 
E) None of the above answers are correct.

A Two-Factor Experiment Where Factor a Consists of I Levels