Data from a Randomized Block Design Are Shown in the Following

question 75

Multiple Choice

Data from a randomized block design are shown in the following table. $\begin{array}{c}\quad\quad\quad\text { Treatment Levels }\\\begin{array}{l}\\\text {Block 1}\\\text {Block 2}\\\text {Block3}\end{array}\begin{array}{l}1 \\8 \\6 \\7 \end{array}\begin{array}{l}2 \\5 \\6 \\8 \end{array}\begin{array}{c}3 \\10 \\9 \\8 \end{array}\begin{array}{r}4\\7\\5\\9\end{array}\end{array}$

Using $\alpha$ = 0.05, the appropriate decision for the blocking effects is ________.

• A)reject the null hypothesis \(\mu\) ₁ \(\ge\) \(\mu\) ₂ \(\ge\) \(\mu\) ₃
• B)do not reject the null hypothesis \(\mu\) ₁ \(\neq\) \(\mu\) ₂ \(\neq\)\(\mu\) ₃
• C)do not reject the null hypothesis \(\mu\)₁=\(\mu\)₂=\(\mu\)₃
• D)reject the null hypothesis \(\mu\) ₁ \(\le\) \(\mu\) ₂ \(\le\) \(\mu\) ₃
• E)do nothing

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Definitions:

Interaction Effect

A statistical concept in which the effect of two or more variables is not simply additive, indicating that these variables interact in predicting a particular outcome.

Main Effect

The overall impact of an independent variable on a dependent variable in an analysis, ignoring the effects of other independent variables.

F Tests

A class of statistical tests used to compare the variances of two or more samples to assess the equality of population variances.

Two-way ANOVA

A statistical test used to determine the effect of two nominal predictor variables on a continuous outcome variable, allowing for interactions between the factors to be analyzed.