A large farm wants to try out a new type of fertilizer to evaluate wether it will increase the farm's maize production. The land is broken into plots that produce an average of 551 kg of maize with a standard deviation of 43 kg per plot.
The owner is interested in detecting any average difference of at least 18 kg per plot.
How many plots of land would be needed for the experiment if the desired power level is 90%?
Assume each plot of land gets treated with either the curent fertilizer or the new fertilizer.
If \( n \) plots are used, then the standard error will be:
\[ SE=\sqrt{\dfrac{43^2}{n}+\dfrac{43^2}{n}}=\dfrac{\sqrt{2}\cdot 43}{\sqrt{n}}=\dfrac{60.8}{\sqrt{n}} \]