A new fertilizer has been discovered! But no one knows how much to put on each a

Question

A new fertilizer has been discovered! But no one knows how much to put on each acre of corn in Nebraska gives the best yield. Also no one knows how much water is needed to get the maximum benefit from the fertilizer. Like most fertilizers this new one can be washed down in the soil past the root zone. Please design the best test design to determine what amount of fertilizer is best for Nebraska soil and corn. It is thought that 100 lbs/acre is a good, but probably too small amount of this new fertilizer. Also state the hypotheses needed in both English and mathematical symbols. Finally, state what statistical tests should be used to analyze the data, include all options given that you do not have the data at this point.

Explanation / Answer

Given that I do not have any data at this point. So for generating the data we have to test this fertilizer on at least 30 diferent patches of soil and observe the effects. The measured variable i.e. lbs/acre will then follow an approximate normal distribution.

Then we will use a t test to validate two hypothesis,

Ho: u>=100 lbs per acre for getting good effects

Ha: u<100 lbs per acre to get good effects

Then when we get the t value using the formula t= x-u/(s/sqrt(n)). we can use this to determine the p value i.e.area under the std. normal curve to the right of this statistic. Then once we fix a level of significance say 0.05, then if p < 0.05, then we reject the null hypothesis and see whatlevel is actually good for Nebraska soil and corn.

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