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. 1) Suppose all assumption of pa

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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.

1) Suppose all assumption of parametric test were satisfied, perform necessary parametric tests of hypothesis at 5% level of significance. 

Test for Interaction of factor A and B

Ho: (in symbols and words) 

Ha: (in symbols and words)  Test statistic formula:  Value of the test statistic:  

p-value:

Decision: 

Conclusion:  

 

Test for factor A: (if necessary)

Ho: (in symbols and words)  

Ha: (in symbols and words)  

Test statistic formula Value of the test statistic:  p-value: 

Decision: 

Conclusion: 

 

Test for factor B: (if necessary)

Ho: (in symbols and words)  Ha: (in symbols and words) Test statistic formula: Value of the test statistic: 

p-value: 

Decision: 

Conclusion: 

 

2) Explain briefly how you should proceed given the result of recent hypothesis tests. 

Method of
Pesticide
Survival Time (in minutes)
Application
A
31
29
30
1
в
28
30
27
A
23
18
20
2
B
17
15
18
Transcribed Image Text:Method of Pesticide Survival Time (in minutes) Application A 31 29 30 1 в 28 30 27 A 23 18 20 2 B 17 15 18
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
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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