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

question 56

Multiple Choice

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.

---

Definitions:

Latin

An ancient Italic language of the Roman Empire, used as the language of scholarship and administration until superseded by vernacular languages but surviving today in certain ecclesiastical and academic contexts.

Greek

Relating to Greece, its people, or their language.

Cyan/o

A prefix in medical terminology denoting the color blue, often used to describe conditions related to inadequate oxygen levels in the blood.

Iso-

A prefix indicating equality, uniformity, or similarity in certain scientific and technical contexts.