A random sample of soil specimens was taken from a large geographic area. The sp

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 alpha = 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?

Explanation / Answer

mean = 3.323

std deviation =2.72

std error mean = .92

1. H0 : mean = 4

    H1 : mean not= 4

2

Graphs can be plotted by chart

and it gives an increasing trend in organic matter

3

After conducting bootstrapping p value obtained was .475 which indicates null hypothesis cannot be rejected

under 5% significance level

.

4

at 95% , we cannot reject H0 without bootstrapping

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