A Farmer Has Five Different Fields $\mu 1$ Be the Mean for Fertilizer

question 31

Essay

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 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 $\mathrm { A } , \mu _ { 2 }$ the mean for fertilizer $\mathrm { B }$ , and $\mu _ { 3 }$ the mean for no fertilizer. In a test of $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ 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.
$\begin{array}{l|c|c|c} & \text { Fertilizer A } & \text { Fertilizer B } & \text { No Fertilizer } \\\hline \text { Field 1 } & 132 & 141 & 128 \\\text { Field 2 } & 136 & 135 & 130 \\\text { Field 3 } & 144 & 147 & 139 \\\text { Field 4 } & 126 & 134 & 122 \\\text { Field 5 } & 130 & 128 & 125\end{array}$

Learn the anatomical landmarks and divisions of the abdominal region.

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Definitions:

Domestic Supply

The total quantity of goods and services produced within a country that are available for domestic consumption or export.

Domestic Demand

The total demand for goods and services within a specific country, reflecting the consumption patterns of its residents.

World Price

The global market price of a product or service, determined by international supply and demand.

International Trade

The exchange of goods and services between countries, allowing for the expansion of markets and access to resources, goods, and services.