Chapter 13, Problem 10E

(a)

To determine

To find: The degree of freedom and outline the ANOVA table with the sources of variance.

Answer to Problem 10E

Solution: The degree of freedom for factor sex is 1 and for age, the degree of freedom is 2. The degree of freedom of interaction factor is 2.

Explanation of Solution

Calculation: For the provided data, the error term can be calculated as:

$\begin{array}{c}\text{Error term}=N-IJ\\ =66-3\times 2\\ =60\end{array}$

The degree of freedom for Sex can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=I-1\\ =2-1\\ =1\end{array}$

The degree of freedom for Age can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=J-1\\ =3-1\\ =2\end{array}$

The degree of freedom for Interaction can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=\left(I-1\right)\left(J-1\right)\\ =1\times 2\\ =2\end{array}$

The ANOVA table with different sources of variance and degree of freedom is as follows:

Sources	Degree of freedom
Sex	1
Age	2
Interaction	2
Error	60
Total	65

(b)

To determine

To find: The degree of freedom and outline the ANOVA table with the sources of variance.

Answer to Problem 10E

Solution: The degree of freedom for week after harvest is 4 and for amount of water, the degree of freedom is 1. The degree of freedom of interaction factor is 4.

Explanation of Solution

Calculation: For the provided data, the error term can be calculated as:

$\begin{array}{c}\text{Error term}=N-IJ\\ =30-10\\ =20\end{array}$

The degree of freedom for Week after harvest can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=I-1\\ =5-1\\ =4\end{array}$

The degree of freedom for Amount of water can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=J-1\\ =2-1\\ =1\end{array}$

The degree of freedom for Interaction can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=\left(I-1\right)\left(J-1\right)\\ =4\times 1\\ =4\end{array}$

The ANOVA table with different sources of variance and degree of freedom is as follows:

Sources	Degree of freedom
Week after harvest	4
Amount of water	1
Interaction	4
Error	20
Total	29

(c)

To determine

To find: The degree of freedom and outline the ANOVA table with the sources of variance.

Answer to Problem 10E

Solution: The degree of freedom for factor mixture is 5 and for freezing/thawing, the degree of freedom is 2. The degree of freedom of interaction factor is 10.

Explanation of Solution

Calculation: For the provided data, the error term can be calculated as:

$\begin{array}{c}\text{Error term}=N-IJ\\ =54-6\times 3\\ =36\end{array}$

The degree of freedom for Mixture can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=I-1\\ =6-1\\ =5\end{array}$

The degree of freedom for freezing /thawing can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=J-1\\ =3-1\\ =2\end{array}$

The degree of freedom for Interaction can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=\left(I-1\right)\left(J-1\right)\\ =5\times 2\\ =10\end{array}$

The ANOVA table with different sources of variance and degree of freedom is as follows:

Sources	Degree of freedom
Mixture	5
freezing/thawing	2
Interaction	10
Error	36
Total	53

(d)

To determine

To find: The degree of freedom and outline the ANOVA table with the sources of variance.

Answer to Problem 10E

Solution: The degree of freedom for factor different colored tags is 3 and for the type of buyers, degree of freedom is 1. The degree of freedom of interaction factor is 3.

Explanation of Solution

Calculation: For the provided data, the error term can be calculated as:

$\begin{array}{c}\text{Error term}=N-IJ\\ =138-4\times 2\\ =130\end{array}$

The degree of freedom for different colored tags can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=I-1\\ =4-1\\ =3\end{array}$

The degree of freedom for the type of buyers can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=J-1\\ =2-1\\ =1\end{array}$

The degree of freedom for Interaction can be calculated as:

$\begin{array}{c}\text{d}\text{.f}=\left(I-1\right)\left(J-1\right)\\ =3\times 1\\ =3\end{array}$

The ANOVA table with different sources of variance and degree of freedom is as follows:

Sources	Degree of freedom
Different colored tags	3
Type of buyers	1
Interaction	3
Error	130
Total	137