SoilCompress.csv

comp	pent
Compressed	2.86
Compressed	2.68
Compressed	2.92
Compressed	2.82
Compressed	2.76
Compressed	2.81
Compressed	2.78
Compressed	3.08
Compressed	2.94
Compressed	2.86
Compressed	3.08
Compressed	2.82
Compressed	2.78
Compressed	2.98
Compressed	3
Compressed	2.78
Compressed	2.96
Compressed	2.9
Compressed	3.18
Compressed	3.16
Intermediate	3.35
Intermediate	3.59
Intermediate	3.31
Intermediate	3.61
Intermediate	3.59
Intermediate	3.35
Intermediate	3.39
Intermediate	3.47
Intermediate	3.17
Intermediate	3.23
Intermediate	3.75
Intermediate	3.57
Intermediate	3.39
Intermediate	3.33
Intermediate	4.07
Intermediate	3.13
Intermediate	3.67
Intermediate	3.65
Intermediate	3.83
Intermediate	4.47
Loose	3.99
Loose	4.2
Loose	3.94
Loose	4.16
Loose	4.29
Loose	4.19
Loose	4.13
Loose	4.41
Loose	3.98
Loose	4.41
Loose	4.11
Loose	4.3
Loose	3.96
Loose	4.03
Loose	4.89
Loose	4.12
Loose	4
Loose	4.34
Loose	4.27
Loose	4.91

Driving heavy equipment on wet soil can compress the soil and make it harder for future crops to grow. The data file SoilCompress.csv contains data on the "penetrability" of the same soil at different levels of compression. The variables are -

comp: the soil compression level for each penetrability measurement. Values are "C" (compressed), "I" (intermediate) or "L" (loose).

pent:soil penetrability measurements in unspecified units.

We are interested in comparing the distributions of soil penetrability observed at the three soil compression levels.

a, What type of variables are comp and pent? In your own words describe these two types of variables referencing comp and pent respectively

b. Provide visualisations that allow the distributions of soil penetrability to be compared between soil compression levels. Construct your graphical comparison using -

i. Boxplots; and

ii. Histograms

c.Do any of the penetrability observations appear to be 'extreme' relative to the compression group in which they occur? Justify your answer and identify any extreme values.

d.Provide the mean & standard deviation and median & IQR for each distribution. Which measures are robust to extreme values and outliers?

e.Using the visualisations and descriptive statistics, compare the three distributions of soil penetrability observations in terms of their locations, spread and shapes.

f.Later in the course we will use statistical tools to compare the three means. Do you think such tools are likely to report a difference? Why? Why not?

2.

a.State your intended major (cybersecurity)

b.Briefly describe a situation in your field where the binomial distribution might be relevant with reference to the five conditions. The example must not come from unit notes or any other MAS183 materials. (Note stating the five conditions only will get 0 marks).

3.

The duration of pregnancy in a particular human population (in a district of South India) is approximately Normally distributed with = 274.3 days and = 8.9 days. In the following questions, assume that this distribution is exact.

a. What proportion of pregnancies last between 265 and 279 days? Your answer must include a diagram and an approximation as well as a precise answer with workings.

b. What durations give the quartiles of the distribution of pregnancy durations for this population?