Question

One of the first uses of some techniques in statistics goes back to 1920s for the purpose of testing the effectiveness of fertilizers on plots of lands. The objective of this exercise was to see if different amounts of fertilizers are yielding different amounts of crops. Recently, a scientist at one of the top agricultural colleges in the U.S. decided to conduct this experiment on some new fertilizers and was interested to see the impact of them on crop yields. Accordingly, she selected three types of fertilizers A, B, and C and applied fertilizer A to 20 1- acre plots of land, fertilizer B to another 20 plots, and fertilizer C to yet another plots of land. At the end of growing season, the crop yields were recorded and is summarized in the data file named:

A) Describe the problem background, objective of study and identify the type of scale of measurement for the data

b) Use appropriate descriptive statistics to explore and summarize the data for fertilizer A and C and compare their results. Remember to interpret the findings accurately and present them in a clear and coherent way.

c) Assuming data for crop yield using fertilizer A, is normally distributed, calculate the parentage of plots of land that yield crops between 492 and 600 units (use only whole numbers in the descriptive statistics)

d) Assuming crop yield (in bushels) using fertilizer A, is distributed normally with a population mean yield of 570 bushels and population standard deviation of 40 bushels, then what is the probability that a randomly selected plot of land can yield more than 600 bushels?

e) Referring to part d, if a randomly selected plot of land is in the top 1 percent crop production, at least how much production should the land have?

Plot	Fertilizer A	Fertilizer B	Fertilizer C
1	563	588	575
2	593	624	593
3	542	576	564
4	649	672	653
5	565	583	556
6	587	612	590
7	595	617	607
8	429	446	423
9	500	515	483
10	610	641	626
11	524	547	523
12	559	586	568
13	546	582	551
14	503	530	502
15	550	573	567
16	492	518	495
17	497	529	513
18	619	643	626
19	473	497	479
20	533	556	540

Answer 1

Note : allowed to solve only 4 sub questions in one post.

A) Describe the problem background, objective of study and identify the type of scale of measurement for the data

We need to check the effectiveness of the fertilizers. Hence we sample out 20 plots and apply Fertilizers A, B, C and then examine the yield due to each fertilizer type.

Scale of measurment for the data - Amount of product is a quantitative variable and measured on the ratio scale which has a perfect zero defined.

b) Use appropriate descriptive statistics to explore and summarize the data for fertilizer A and C and compare their results. Remember to interpret the findings accurately and present them in a clear and coherent way.

Step 1 : Input the data in excel as shown

Step 2 : Go to Data -> DAta analysis -> Descriptive Statistics

Step 3 : Input the data as shown.

Step 4 : Output will be generated as follows.

We see that produced due to Fertilizer A is has a mean of 546.45 with a standard deviation of 54.35 and median values 548.
On the other hand, Fertilizer C is has a mean of 551.7 with a standard deviation of 57.79 and median values 560

It seems that the Fertilizer C is more effective than A, but we need to test it statistically by doing a hypothesis testing.

c) Assuming data for crop yield using fertilizer A, is normally distributed, calculate the parentage of plots of land that yield crops between 492 and 600 units (use only whole numbers in the descriptive statistics)

d) Assuming crop yield (in bushels) using fertilizer A, is distributed normally with a population mean yield of 570 bushels and population standard deviation of 40 bushels, then what is the probability that a randomly selected plot of land can yield more than 600 bushels?