Question
Directions: This is NOT a group activity. Every student must complete this assignment. You will be graded on how well you demonstrate and apply your knowledge of the statistical concepts and procedures. Agriculture: Bell Peppers The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are commercial crop, this disease has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first step in the research project is to compare the mean soil water content for the two fields (Source: Journal of Agricultural, Biological, and Environmental Statistics, Vol. 2, No. 2). Units are percent water by volume of soil. Field A Samples, x_1: 10.2, 10.7, 15.5, 10.4, 9.9, 10.0, 16.6, 15.1, 15.2, 13.8, 14.1, 11.4, 11.5, and 11.0. Field B samples, x_2: 8.1, 8.5, 8.4, 7.3, 8.0, 7.1, 13.9, 12.2, 13.4, 11.3, 12.6, 12.6, 12.7, 12.4, 11.3 and 12.5. For this assignment, complete the following: What is the goal of this study? Define the main variable. What constitutes the population of this study? What is the sample size? Compute the mean, median, and standard deviation of each data set. Draw appropriate graphs for each data set (boxplots are recommended). Include a graph comparing the means and standard deviations of the two data sets. Use EXCEL to generate these graphs. Write a paragraph describing the similarities and differences between the two data sets, using appropriate descriptive statistics such as means, median, standard deviation, etc. Assuming the distribution of soil water content in each field is mound-shaped and symmetric, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B. Let: mu_1 = mean soil water content for Field A mu_2 = mean soil water content for Field B
Explanation / Answer
Part (a)
Goal of study: To assess the role of water content in soil in aiding spread of pathogen. ANSWER
Part (b)
Main variable: Percent water by volume of soil ANSWER
Part (c)
The population: Agricultural fields cultivating the commercial crop ball pepper.
Sample size: 14 for Field A and 16 for Field B. ANSWER
Part (d)
Field
Sample size
Mean
Median
Standard Deviation
A
14
12.53
11.45
2.31
B
16
10.77
11.75
2.32
Details of Excel Calculations are given below for reference:
Field A
I
XI
xi^2
1
11
121
2
10.2
104.04
3
10.7
114.49
4
15.5
240.25
5
10.4
108.16
6
9.9
98.01
7
10
100
8
16.6
275.56
9
15.1
228.01
10
15.2
231.04
11
13.8
190.44
12
14.1
198.81
13
11.4
129.96
14
11.5
132.25
n =
14
Sum
175.4
Mean
12.52857
Sum Xi^2
2272.02
Variance
5.322041
SD
2.306955
Field B
I
XI
xi^2
1
11.3
127.69
2
12.5
156.25
3
8.1
65.61
4
8.5
72.25
5
8.4
70.56
6
7.3
53.29
7
8
64
8
7.1
50.41
9
13.9
193.21
10
12.2
148.84
11
13.4
179.56
12
11.3
127.69
13
12.6
158.76
14
12.6
158.76
15
12.7
161.29
16
12.4
153.76
n =
16
Sum
172.3
Mean
10.76875
Sum Xi^2
1941.93
Variance
5.404648
SD
2.32479
Field
Sample size
Mean
Median
Standard Deviation
A
14
12.53
11.45
2.31
B
16
10.77
11.75
2.32
