Give the ANOVA model for the design in the given form.

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

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Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Answer 6

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Answer 7

Chapter 26, Problem 1E

To determine

Give the ANOVA model for the design in the given form.

Answer 8

Expert Solution & Answer

Answer to Problem 1E

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

It is given that there are two factors, Sex and Athlete, in analyzing TV watching by students.

The ANOVA model:

In the ANOVA model, each observation is broken into sum of the grand mean, the treatment effect, and an error. The general model for ANOVA for the i^th observation is as follows:

yij=μ+τj+εij,where, μ is the grand mean, τj is the treatment effect, andεij is the error.

Here, the two factors are Sex and Athlete.

Denote τ as the treatment effect of the i^th observation at level j of factor “Sex” and γ as the treatment effect of i^th observation at level k of the factor “Athlete”. There are 2 levels in factor “Sex” and 4 levels in factor “Athelete”. That is, j takes values 1 and 2 and k takes values 1, 2, 3, and 4.

The ANOVA model for the design in the given form is yijk=μ+τj+γk+εijk.