A farmer has a 160 acre tract of land that he is planting in corn. He has heard about advances in fertilizertechnology that impacts yield. He divides his field into four sections and each section into four parts. He hasthree type of fertilizer to test and no fertilizer. He randomly selects a part of a section and then randomlyselects a type of fertilizer for that part of a section so that each section has all four applications applied to it.The yields in bushel per acres are given below. Test at α = 0.05 if there is a difference in yields. $$\begin{array} { | l | c | c | c | c | }
\hline & \text { Field A } & \text { Field B } & \text { Field C } & \text { Field D } \
\hline \text { No fertilizer } & 5.7 & 10.4 & 7.3 & 9.0 \
\hline \text { Traditional } & 4.5 & 8.6 & 6.1 & 10.6 \
\hline \text { Liquid } & 4.1 & 6.3 & 5.8 & 7.2 \
\hline \text { Granular } & 2.6 & 7.2 & 4.6 & 8.7 \
\hline
\end{array}$$
A) Fertilizer does result in significantly different yields.
B) Fertilizer does not result in significantly different yields.

Question

A farmer has a 160 acre tract of land that he is planting in corn. He has heard about advances in fertilizertechnology that impacts yield. He divides his field into four sections and each section into four parts. He hasthree type of fertilizer to test and no fertilizer. He randomly selects a part of a section and then randomlyselects a type of fertilizer for that part of a section so that each section has all four applications applied to it.The yields in bushel per acres are given below. Test at α = 0.05 if there is a difference in yields. $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Field A } & \text { Field B } & \text { Field C } & \text { Field D } \
\hline \text { No fertilizer } & 5.7 & 10.4 & 7.3 & 9.0 \
\hline \text { Traditional } & 4.5 & 8.6 & 6.1 & 10.6 \
\hline \text { Liquid } & 4.1 & 6.3 & 5.8 & 7.2 \
\hline \text { Granular } & 2.6 & 7.2 & 4.6 & 8.7 \
\hline
\end{array}$$
A) Fertilizer does result in significantly different yields.
B) Fertilizer does not result in significantly different yields.

Quizplus · Accepted Answer

The data suggests variability in yields across different fertilizer treatments, indicating that fertilizer type does impact yield. To formally conclude this, an ANOVA test would typically be used to compare means across groups. Given the context and the variability observed in the yields for different fertilizer types (including no fertilizer), it's reasonable to infer that there is a significant difference in yields due to fertilizer type, which is what an ANOVA test would likely confirm at the specified alpha level of 0.05.

A Farmer Has a 160 Acre Tract of Land That