Conduct Analysis of Variance on the Randomized Complete Block Design $\mathrm { A }$

question 44

Short Answer

Conduct Analysis of Variance on the Randomized Complete Block Design
-A farmer has five different fields. He wishes to test two different fertilizers. The yields of corn may vary from field to field depending on a number of factors such as soil quality, sunlight etc. He divides each field into three sections. For each field, he randomly assigns one of the sections to receive fertilizer $\mathrm { A }$ , one of the sections to receive fertilizer $B$ , and one of the sections to receive no fertilizer. At harvest time, he records the corn yields in bushels per acre for each section of each field. The results are shown in the table. Let $\mu _ { 1 }$ be the mean for fertilizer $A , \mu _ { 2 }$ the mean for fertilizer $B$ , and $\mu _ { 3 }$ the mean for no fertilizer. In a test of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ versus $\mathrm { H } _ { 1 }$ : at least one of the means is different, the null hypothesis is rejected at the $\alpha = 0.05$ level of significance. Use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$ . Give the P-value for each of the pairwise tests and state your conclusion.
$\begin{array}{l|c|c|c} & \text { Fertilizer A } & \text { Fertilizer B } & \text { No Fertilizer } \\\hline \text { Field 1 } & 132 & 141 & 128 \\\text { Field 2 } & 136 & 135 & 130 \\\text { Field 3 } & 144 & 147 & 139 \\\text { Field 4 } & 126 & 134 & 122 \\\text { Field 5 } & 130 & 128 & 125\end{array}$

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Definitions:

Structure

The arrangement or organization of atoms within a molecule, determining its shape and properties.

Cope Elimination

A reaction where an amine oxide is heated, leading to the elimination of a hydroxylamine and the formation of an alkene.

Amine Oxide

A compound featuring an amine group bonded to an oxygen atom, typically formed by the oxidation of amines.

Quaternary Ammonium Salt

A compound containing a nitrogen atom bonded to four alkyl groups, with a positive charge balanced by a negatively charged anion.