In agriculture, there are a lot of factors that determine the yield performance from the harvest. You are an agricultural quality engineer working with 3 different fertilizers to be introduced to the Indian market. As you have investigated, there are seven different types of soil deposits in India. They are alluvial soil, black soil, red soil, laterite soil, arid soil, forest soil and marsh soil. These soils are formed by the sediments brought down by the rivers. They are also have varied chemical properties. The following parameters are known to be important chemical compositions to act upon barley harvest

Al: Percentage of aluminum oxide in soil sample

Fe: Percentage of iron oxide in soil sample

Mg: Percentage of magnesium oxide in soil sample

Ca: Percentage of calcium oxide in soil sample

Na: Percentage of sodium oxide in soil sample

Since India is very big in area, you have taken 4500 soil samples from all 7 different types of soils and have measured their chemical composition. Later using all of these soils as possible areas of the plantation. You have grown barley in a laboratory environment with and without the fertilizer and have measured the grain size as the critical output at the end of 30 days of growth under controlled laboratory conditions like light, humidity, and temperature. Since there are 3 different fertilizer types, you want to find out the one that gives the maximum grain size to fulfill your objective function. As the expert of the process, you are willing to take 10 % alpha risk and 20% beta risk. The data is recorded in India_soil.mpj

A. Are the distributions of chemical concentrations normally distributed? Why or why not?

B. What is the Confidence interval of the mean and standard deviation of chemical concentrations in all different type of soils?

C. Are the standard deviations of chemical compositions varying with respect to soil types? Report with p-values and also show the distribution of data with graphical tools and comment

D. Are the averages of chemical compositions varying with respect to soil types? Report with p-values and also show the distribution of data with graphical tools and comment

E. Write down the two hypotheses that you want to test in questions c and d?

F. Write down and test the assumptions that you have made when you have used in question d?

G. How do the alpha and beta risk levels influence the analysis results?

H. What is the difference that you could have seen in Al concentration that you could have seen between the averages of soil types with your sample set?

I. If the majority of the current farmers in India are not using fertilizers, which soil type is most advantageous in terms of providing the maximum grain size?

J. What is the expected grain size average and standard deviation with the best soil type?

K. Are any of the 3 types of fertilizers improving grain size in terms of average or variation? Why or why not?

L. What is the mean difference that you could have seen in the means with different fertilizer types?

M. Is there a relationship between the chemical composition and grain size?

N. What is the executive report that you will provide to your managers?

india_soil.MPJ