Problem: Mr. Kinalabaw, an owner of a mango plantation, is worried about the increasing number of fruit piercing moths present in most of the mango trees in his farm. He then asked for Concon’s help, his trusted statistician, in resolving the problem. They identified two types of pesticide (1, 2) and two methods of application (A, B). They applied each treatment combination to 3 fruit piercing moths. Their survival time (in minutes) was recorded. Pesticide Method of
Problem: Mr. Kinalabaw, an owner of a mango plantation, is worried about the increasing number of fruit piercing moths present in most of the mango trees in his farm. He then asked for Concon’s help, his trusted statistician, in resolving the problem. They identified two types of pesticide (1, 2) and two methods of application (A, B). They applied each treatment combination to 3 fruit piercing moths. Their survival time (in minutes) was recorded. Pesticide Method of
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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FRUIT PIERCING MOTHS
Problem: Mr. Kinalabaw, an owner of a mango plantation, is worried about the increasing number of fruit piercing moths present in most of the mango trees in his farm. He then asked for Concon’s help, his trusted statistician, in resolving the problem. They identified two types of pesticide (1, 2) and two methods of application (A, B). They applied each treatment combination to 3 fruit piercing moths. Their survival time (in minutes) was recorded.
| Pesticide | Method of Application | Survival Time (in minutes) | ||
| 1 | 31 | 29 | 30 | |
| 28 | 30 | 27 | ||
| 2 | 23 | 18 | 20 | |
| 27 | 15 | 18 |
1) Identify the factors, factor levels, treatment combinations, experimental units, response variable, and blocking factor (if any).
- factors and factor levels: _________________________
- treatment combinations: _________________________
- experimental units: _________________________
- response variable: _________________________
- design structure: _________________________
2) Specify the appropriate linear model and define each component in the context with the problem.
?!"# = ? + ?! + ?" + (??)!" + ?!"#; ? = 1,2 ; ? = 1,2 ; ? = 1,2,3
Yijk=
µ=
ai=
bj=
(ab)ij =
eijk =
Transcribed Image Text:FRUIT PIERCING MOTHS PROBLEM
data: Pesticide 1 Method A
Pesticide 1 Method B
Shapiro-Wilk normality test
W = 1.00000,
p-value = 1.0000
data:
Shapiro-Wilk normality test
W - 0.96429,
p-value - 0.6369
Pesticide 2 Method A data:
Pesticide 2 Method B
data:
Shapiro-Wilk normality test
W = 0.98684
p-value = 0.7804
Shapiro-Wilk normality test
W- 0.96429
p-value - 0.6369
Bartlett test of homogeneity of variances
data: survival_time by trmcombin
Bartlett's K-squared = 1.4136, df = 3, p-value = 0.7024
Levene's Test for Homogeneity of Variance (center - "mean")
Df F value Pr (>F)
group
3
0.8718 0.4947
Anova Table (Type II tests)
Response: survival_time
Pr (>F)
0.02851 *
Sum Sq Df F value
method
pesticide
method:pesticide
Residuals
21.33 1
7.1111
1 113.7778 0.000005232 ***
0.34659
341.33
3.00
1
1.0000
24.00
Signif. codes:
O *** 0.001 '** 0.01 ** 0.05 '.' 0.1
Kruskal-Wallis rank sum test
data:
survival_time by trmcombin
Kruskal-Wallis chi-squared - 9.6573, df - 3, p-value - 0.02172
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