Respuesta :
Answer:
a) [tex]df_{num}=k-1=5-1=4[/tex]
b) [tex]df_{den}=N-k=77-5=72[/tex]
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:
[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]
[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
And we have this property
[tex]SST=SS_{between}+SS_{within}[/tex]
The degrees for the numerator are [tex]df_{num}=k-1=5-1=4[/tex], where k represent the number of groups on this case k =5.
The degrees for the denominator are [tex]df_{den}=N-k=77-5=72[/tex], where N represent the total number of people N=17+15+16+18+11=77.
And the total degrees of freedom are given by: [tex]df_{tot}=df_{num}+df_{den}=N-1=4+72=76[/tex]
