  A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22A soil scientist wants to know whether the population mean percent organic matter is different than 4%. Asignificance level of α = 0.05 is chosen.(a)  State hypotheses appropriate to the research question.(b)  Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?(c)  Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?(d)  Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)(e)  Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?Thank you so much in advance for helping with this question!

Question

A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.

1. (a)  State hypotheses appropriate to the research question.
2. (b)  Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
3. (c)  Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
4. (d)  Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
5. (e)  Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?

Thank you so much in advance for helping with this question!

Step 1

Note:

Hi there! Thank you for posting the question. As your question has more than 3 parts, we have solved three parts for you. Due to complexity levels, we are unable to solve part (c), that is, the part involving 8,000 bootstrap resamplings.

Step 2

Part (a): Hypotheses:

Denote μ as the true population mean percentage of organic matter in the soil. The hypotheses appropriate to the research question are as follows:

Null hypothesis:

H0: μ = 4; that is, the true population mean percentage of organic matter in the soil is 4%.

Alternate hypothesis:

H1: μ ≠ 4; that is, the true population mean percentage of organic matter in the soil is different from 4%.

Step 3

Part (b): Graph:

We have decided to draw a line diagram, with the percentage of organic matter in the specimens of soil in the y-axis and the specimen number (1 to 8) in the x-axis.

The line diagram, with markers for the actual data values, is a simple graph that is easy to interpret. It is quite easy to spot the hypothesized mean value of 4 by merely observing the y-axis. Thereafter, one can simply count the number of observations below and above 4, to form...

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