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An experiment has been conducted for four treatments with seven blocks. Complete the following analysis of variance table. (Round your values for mean squares and F to two decimal places and your p-value to three decimal places.) Sum Source of Variation Degrees of Freedom Mean Square F of Squares p-value Treatments 1,500 Blocks 400 Error Total 2.500 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. ⒸH₂H₂ = H₂=H₂ =H₂ OH₂H₂H₂H₂ # H₂ H₂H₁ H₂H₂ = H₂ OH: At least two of the population means are equal. H: At least two of the population means are different. OH: Not all the population means are equal. OH₂H₂ =H₂=H₂ = H₂ H₂: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value= State your conclusion. O Reject H. There is not sufficient evidence to conclude that the means of the four treatments are not all equal. O Reject H. There is sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject H. There is not sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject H. There is sufficient evidence to conclude that the means of the four treatments are not all equal.

An experiment has been conducted for four treatments with seven blocks. Complete the following analysis of variance table. (Round your values for mean squares and F to two decimal places and your p-value to three decimal places.) Sum Source of Variation Degrees of Freedom Mean Square F of Squares p-value Treatments 1,500 Blocks 400 Error Total 2.500 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. ⒸH₂H₂ = H₂=H₂ =H₂ OH₂H₂H₂H₂ # H₂ H₂H₁ H₂H₂ = H₂ OH: At least two of the population means are equal. H: At least two of the population means are different. OH: Not all the population means are equal. OH₂H₂ =H₂=H₂ = H₂ H₂: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value= State your conclusion. O Reject H. There is not sufficient evidence to conclude that the means of the four treatments are not all equal. O Reject H. There is sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject H. There is not sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject H. There is sufficient evidence to conclude that the means of the four treatments are not all equal.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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# ANOVA Analysis for Four Treatments An experiment has been conducted for four treatments with seven blocks. Complete the following analysis of variance table by rounding your values for mean squares and F to two decimal places, and your p-value to three decimal places. | **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **F** | **p-value** | |-------------------------|--------------------|------------------------|-----------------|-------|-------------| | **Treatments** | 1,500 | | | | | | **Blocks** | 400 | | | | | | **Error** | | | | | | | **Total** | 2,500 | | | | | ### Instructions 1. Use a significance level of α = 0.05 to test for any significant differences. 2. State the null and alternative hypotheses using the notation below: - \( H_0 \): \(\mu_1 = \mu_2 = \mu_3 = \mu_4\) - \( H_1 \): \(\mu_1 \neq \mu_2 \neq \mu_3 \neq \mu_4\) #### Hypotheses Detail - Null Hypothesis (\(H_0\)): All the population means are equal. - Alternative Hypotheses (\(H_1\)): 1. \(H_{1a}\): At least two of the population means are equal. 2. \(H_{1b}\): At least two of the population means are different. 3. \(H_{1c}\): Not all the population means are equal. 4. \(H_{1d}\): At least two of the population means are equal. #### Steps 3. Find the value of the test statistic: - Round your answer to two decimal places. 4. Find the p-value: - Round your answer to three decimal places. ```plaintext p-value = ____ ``` 5. State your conclusion based on the p-value: - Reject \(H_0\). There is sufficient evidence to conclude that the means of the four treatments are not all equal. - Do not reject \(H_0\). There is not sufficient evidence to conclude that the means
Transcribed Image Text:# ANOVA Analysis for Four Treatments An experiment has been conducted for four treatments with seven blocks. Complete the following analysis of variance table by rounding your values for mean squares and F to two decimal places, and your p-value to three decimal places. | **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **F** | **p-value** | |-------------------------|--------------------|------------------------|-----------------|-------|-------------| | **Treatments** | 1,500 | | | | | | **Blocks** | 400 | | | | | | **Error** | | | | | | | **Total** | 2,500 | | | | | ### Instructions 1. Use a significance level of α = 0.05 to test for any significant differences. 2. State the null and alternative hypotheses using the notation below: - \( H_0 \): \(\mu_1 = \mu_2 = \mu_3 = \mu_4\) - \( H_1 \): \(\mu_1 \neq \mu_2 \neq \mu_3 \neq \mu_4\) #### Hypotheses Detail - Null Hypothesis (\(H_0\)): All the population means are equal. - Alternative Hypotheses (\(H_1\)): 1. \(H_{1a}\): At least two of the population means are equal. 2. \(H_{1b}\): At least two of the population means are different. 3. \(H_{1c}\): Not all the population means are equal. 4. \(H_{1d}\): At least two of the population means are equal. #### Steps 3. Find the value of the test statistic: - Round your answer to two decimal places. 4. Find the p-value: - Round your answer to three decimal places. ```plaintext p-value = ____ ``` 5. State your conclusion based on the p-value: - Reject \(H_0\). There is sufficient evidence to conclude that the means of the four treatments are not all equal. - Do not reject \(H_0\). There is not sufficient evidence to conclude that the means
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