Please show all work and explain how you got your answers. 2. The table below co

Question

Please show all work and explain how you got your answers.

2. The table below contains data on the enzyme activity of mannose-6-phosphate isomerase (MPI) for three different genotypes (SS, FS, FF) in the amphipod crustacean Platorchestia platensis. Because the effects of sex are not known, specimens were classified by sex. Conduct a two-way ANOVA on this dataset. Test for effect of genotype, the effect of sex, and whe Show all calculations and state your conclusions. ther there is an interaction effect between two factors. Replace the letters A-B-C-D-E-F in the table with the last six numbers of y number FS FI Females 3.6A 3.5B 3.9C 4.26 2.89 3.22 2.74 3.16 3.51 4.11 3.34 4.02 3.25 3.91 3.87 Males 2.8D 3.6E 4.9F 3.98 3.41 3.21 3.11 3.99 3.47 3.15 3.69 4.01 3.72 4.15

Explanation / Answer

We use R coding for calculations.

We test hypothesis first as:

H01: interaction = 0 vs H11: H01 is false.

Then we test for effect of sex and genotype

model1<- aov(Data ~ Sex * Genotype, data = data3)
> model1
Call:
aov(formula = Data ~ Sex * Genotype, data = data3)

Terms:
Sex Genotype Sex:Genotype Residuals
Sum of Squares 0.158413 4.202447 0.090847 2.694440
Deg. of Freedom 1 2 2 24

Residual standard error: 0.3350647
Estimated effects may be unbalanced
> summary(model1)
Df Sum Sq Mean Sq F value Pr(>F)   
Sex 1 0.158 0.1584 1.411 0.247   
Genotype 2 4.202 2.1012 18.716 1.26e-05 ***
Sex:Genotype 2 0.091 0.0454 0.405 0.672   
Residuals 24 2.694 0.1123

We see that Genotype has significant effect at all level of significance whereas interaction effect and sex effect is null.

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