5) 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) Σ ij (aß) ij = 0: There is no interaction between the type of pesticide used and its method of application. Ha: (in symbols and words) Σij (aß) ij 0: There is an interaction between the type of

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

5) 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) Σ ij (aß)ij = 0: There is no interaction between the type of
pesticide used and its method of application.
Ha: (in symbols and words) Σ ij (aß)ij = 0: There is an interaction between the type of
pesticide used and its method of application.
Test statistic formula: MSAB
MSE
Value of the test statistic: 1.000
p-value: 0.34659
Decision: Since 0.34659 > 0.05, we fail to reject Ho.
Conclusion: At 5% level of significance, there is no sufficient evidence to say that there is an
interaction between the type of pesticide used and its method of application.
Test for factor A: (if necessary)
Ho: (in symbols and words) Σ i ai = 0: There is no difference in the mean survival time (in
mins) among the different types of pesticides used.
Ha: (in symbols and words) Σi ai = 0: At least one type of pesticide used has a different
survival time (in mins).
Test statistic formula: MSE
MSA
Transcribed Image Text:5) 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) Σ ij (aß)ij = 0: There is no interaction between the type of pesticide used and its method of application. Ha: (in symbols and words) Σ ij (aß)ij = 0: There is an interaction between the type of pesticide used and its method of application. Test statistic formula: MSAB MSE Value of the test statistic: 1.000 p-value: 0.34659 Decision: Since 0.34659 > 0.05, we fail to reject Ho. Conclusion: At 5% level of significance, there is no sufficient evidence to say that there is an interaction between the type of pesticide used and its method of application. Test for factor A: (if necessary) Ho: (in symbols and words) Σ i ai = 0: There is no difference in the mean survival time (in mins) among the different types of pesticides used. Ha: (in symbols and words) Σi ai = 0: At least one type of pesticide used has a different survival time (in mins). Test statistic formula: MSE MSA
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)
A
31
29
30
1
B
28
30
27
A
23
18
20
2
B
17
15
18
185
data: Pesticide 1 Method A
Shapiro-Wilk normality test
W = 1.00000,
p-value = 1.0000
data: Pesticide 2 Method A
Shapiro-Wilk normality test
W 0.98684
p-value 0.7804
=
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
8
Anova Table (Type II tests)
Response: survival time
Sum Sq Df F value
21.33 1 7.1111
method
pesticide
method:pesticide 3.00 1 1.0000
Residuals
24.00 8
Pr (>F)
0.02851 *
341.33 1 113.7778 0.000005232 ***
0.34659
Signif. codes: 0 ***** 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
data: Pesticide 1 Method B
Shapiro-Wilk normality test
W 0.96429,
p-value 0.6369
data: Pesticide 2 Method B
Shapiro-Wilk normality test
W= 0.96429
p-value 0.6369
Transcribed Image Text: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) A 31 29 30 1 B 28 30 27 A 23 18 20 2 B 17 15 18 185 data: Pesticide 1 Method A Shapiro-Wilk normality test W = 1.00000, p-value = 1.0000 data: Pesticide 2 Method A Shapiro-Wilk normality test W 0.98684 p-value 0.7804 = 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 8 Anova Table (Type II tests) Response: survival time Sum Sq Df F value 21.33 1 7.1111 method pesticide method:pesticide 3.00 1 1.0000 Residuals 24.00 8 Pr (>F) 0.02851 * 341.33 1 113.7778 0.000005232 *** 0.34659 Signif. codes: 0 ***** 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 data: Pesticide 1 Method B Shapiro-Wilk normality test W 0.96429, p-value 0.6369 data: Pesticide 2 Method B Shapiro-Wilk normality test W= 0.96429 p-value 0.6369
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