Explain why the F -ratio is expected to be near 1.00 the null hypothesis is true.

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Answer 1

Textbook Question

Chapter 12, Problem 1P

Explain why the F-ratio is expected to be near 1.00 the null hypothesis is true.

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

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Answer 2

Textbook Question

Chapter 12, Problem 1P

Explain why the F-ratio is expected to be near 1.00 the null hypothesis is true.

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

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Answer 3

Textbook Question

Chapter 12, Problem 1P

Explain why the F-ratio is expected to be near 1.00 the null hypothesis is true.

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

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Answer 4

Textbook Question

Chapter 12, Problem 1P

Explain why the F-ratio is expected to be near 1.00 the null hypothesis is true.

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

Answer 8

Expert Solution & Answer

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer 12

Answer to Problem 1P

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Answer 13

Explanation of Solution

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

Answer 14

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Explain why the F -ratio is expected to be near 1.00 the null hypothesis is true.

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Answer to Problem 1P

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