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.
Thank you so much in advance for helping with this question!
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.
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:
H_{0}: μ = 4; that is, the true population mean percentage of organic matter in the soil is 4%.
Alternate hypothesis:
H_{1}: μ ≠ 4; that is, the true population mean percentage of organic matter in the soil is different from 4%.
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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