A large farm wants to try out a new type of fertilizer to evaluate whether it will improve the farm's corn production. The land is broken into plots that produce an average of 1,215 pounds of corn with a standard deviation of 94 pounds per plot. The owner is interested in detecting any average difference of at least 40 pounds 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 current fertilizer or the new fertilizer

Question

Mathematics

Kyan Holmes

13 December, 18:48

A large farm wants to try out a new type of fertilizer to evaluate whether it will improve the farm's corn production. The land is broken into plots that produce an average of 1,215 pounds of corn with a standard deviation of 94 pounds per plot. The owner is interested in detecting any average difference of at least 40 pounds 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 current fertilizer or the new fertilizer

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Wilber · Answer 1

N = 116 plots of land would be needed for the experiment if the desired power level is 90%

Step-by-step explanation:

A large farm wants to try a new fertilizer to evaluate wether it will improve the farm's yield. The land is broken into identical sized plots that produce an average of 1,215lbs/plot of beans with a SD=94lbs/plot. The owner is interested in detecting any average difference of at least 40lbs/plot. How many plots would be needed for the experiment if the desired power level is 90%?

alpha / 2 = 0.48 Z = 0.05

N = [ 0.05 * 94 / 40 ] ^2

N = 116