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You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use a = 0.05. xj Treatment 1 63 46 53 46 52 64.67 Treatment 2 Ho: H₁ H₂ H3 H₂H₁ = H₂=H3 83 71 87 71 78 68.00 Treatment 3 70 54 61 51 59 71.33 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. OH₁ H₁ = H₂=H3 H: Not all the population means are equal. O Ho: Not all the population means are equal. на: Н1 = H2 = из O Ho: At least two of the population means are equal. H: At least two of the population means are different. о но: H1 =H2=Из H₂H₁ H₂ H3 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 Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. (b) Use Fisher's LSD procedure to determine which means are different. Find the value of LSD. (Round your answer to two decimal places.) LSD =

You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use a = 0.05. xj Treatment 1 63 46 53 46 52 64.67 Treatment 2 Ho: H₁ H₂ H3 H₂H₁ = H₂=H3 83 71 87 71 78 68.00 Treatment 3 70 54 61 51 59 71.33 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. OH₁ H₁ = H₂=H3 H: Not all the population means are equal. O Ho: Not all the population means are equal. на: Н1 = H2 = из O Ho: At least two of the population means are equal. H: At least two of the population means are different. о но: H1 =H2=Из H₂H₁ H₂ H3 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 Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. (b) Use Fisher's LSD procedure to determine which means are different. Find the value of LSD. (Round your answer to two decimal places.) LSD =

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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**Webasssign.net Instructions for ANOVA Analysis and Fisher's LSD Test** **Date: Sun Oct 22** You may need to use appropriate technology to answer this question. ### Data Summary The data are from a completely randomized design. In these calculations, use \(\alpha = 0.05\). | | Treatment 1 | Treatment 2 | Treatment 3 | |-----------|-------------|-------------|-------------| | **Row 1** | 63 | 83 | 70 | | **Row 2** | 46 | 71 | 54 | | **Row 3** | 57 | 87 | 61 | | **Row 4** | 46 | 71 | 51 | - **Mean (\(\bar{x}_j\))** - Treatment 1: 52 - Treatment 2: 78 - Treatment 3: 59 - **Variance (\(s_j^2\))** - Treatment 1: 64.67 - Treatment 2: 68.00 - Treatment 3: 71.33 ### Analysis #### (a) ANOVA Test for Mean Differences Use analysis of variance to test for a significant difference among the means of the three treatments. **State the Null and Alternative Hypotheses:** - Options: 1. \(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a:\) Not all the population means are equal. 2. \(H_0: \mu_1 \neq \mu_2 \neq \mu_3\) \(H_a: \mu_1 = \mu_2 = \mu_3\) 3. \(H_0:\) Not all population means are equal. \(H_a: \mu_1 = \mu_2 = \mu_3\) 4. \(H_0:\) At least two of the population means are equal. \(H_a:\) At least two of the population means are different. 5. \(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1 \neq \mu
Transcribed Image Text:**Webasssign.net Instructions for ANOVA Analysis and Fisher's LSD Test** **Date: Sun Oct 22** You may need to use appropriate technology to answer this question. ### Data Summary The data are from a completely randomized design. In these calculations, use \(\alpha = 0.05\). | | Treatment 1 | Treatment 2 | Treatment 3 | |-----------|-------------|-------------|-------------| | **Row 1** | 63 | 83 | 70 | | **Row 2** | 46 | 71 | 54 | | **Row 3** | 57 | 87 | 61 | | **Row 4** | 46 | 71 | 51 | - **Mean (\(\bar{x}_j\))** - Treatment 1: 52 - Treatment 2: 78 - Treatment 3: 59 - **Variance (\(s_j^2\))** - Treatment 1: 64.67 - Treatment 2: 68.00 - Treatment 3: 71.33 ### Analysis #### (a) ANOVA Test for Mean Differences Use analysis of variance to test for a significant difference among the means of the three treatments. **State the Null and Alternative Hypotheses:** - Options: 1. \(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a:\) Not all the population means are equal. 2. \(H_0: \mu_1 \neq \mu_2 \neq \mu_3\) \(H_a: \mu_1 = \mu_2 = \mu_3\) 3. \(H_0:\) Not all population means are equal. \(H_a: \mu_1 = \mu_2 = \mu_3\) 4. \(H_0:\) At least two of the population means are equal. \(H_a:\) At least two of the population means are different. 5. \(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1 \neq \mu
### ANOVA Analysis and Fisher's LSD Procedure #### Test Statistic and Hypothesis Testing 1. **Find the value of the test statistic.** *(Round your answer to two decimal places.)* - Input box for the test statistic value. 2. **Find the p-value.** *(Round your answer to three decimal places.)* - Input box for the p-value. 3. **State your conclusion.** - **Options:** - Reject \( H_0 \). There is not sufficient evidence to conclude that the means of the three treatments are not equal. - Do not reject \( H_0 \). There is not sufficient evidence to conclude that the means of the three treatments are not equal. - Reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal. - Do not reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal. #### Fisher's LSD Procedure (b) **Determine which means are different.** 1. **Find the value of LSD.** *(Round your answer to two decimal places.)* - Input box for LSD (Least Significant Difference) value. 2. **Calculate the pairwise absolute differences between sample means for each pair of treatments.** - \( | \bar{x}_1 - \bar{x}_2 | = \) - Input box for the calculated difference. - \( | \bar{x}_1 - \bar{x}_3 | = \) - Input box for the calculated difference. - \( | \bar{x}_2 - \bar{x}_3 | = \) - Input box for the calculated difference. 3. **Which treatment means differ significantly?** *(Select all that apply.)* - There is a significant difference between the means for treatments 1 and 2. - There is a significant difference between the means for treatments 1 and 3. - There is a significant difference between the means for treatments 2 and 3. - There are no significant differences. This educational content guides students through analyzing variance (ANOVA) data to determine statistical significance and understand which treatments differ using Fisher's LSD method.
Transcribed Image Text:### ANOVA Analysis and Fisher's LSD Procedure #### Test Statistic and Hypothesis Testing 1. **Find the value of the test statistic.** *(Round your answer to two decimal places.)* - Input box for the test statistic value. 2. **Find the p-value.** *(Round your answer to three decimal places.)* - Input box for the p-value. 3. **State your conclusion.** - **Options:** - Reject \( H_0 \). There is not sufficient evidence to conclude that the means of the three treatments are not equal. - Do not reject \( H_0 \). There is not sufficient evidence to conclude that the means of the three treatments are not equal. - Reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal. - Do not reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal. #### Fisher's LSD Procedure (b) **Determine which means are different.** 1. **Find the value of LSD.** *(Round your answer to two decimal places.)* - Input box for LSD (Least Significant Difference) value. 2. **Calculate the pairwise absolute differences between sample means for each pair of treatments.** - \( | \bar{x}_1 - \bar{x}_2 | = \) - Input box for the calculated difference. - \( | \bar{x}_1 - \bar{x}_3 | = \) - Input box for the calculated difference. - \( | \bar{x}_2 - \bar{x}_3 | = \) - Input box for the calculated difference. 3. **Which treatment means differ significantly?** *(Select all that apply.)* - There is a significant difference between the means for treatments 1 and 2. - There is a significant difference between the means for treatments 1 and 3. - There is a significant difference between the means for treatments 2 and 3. - There are no significant differences. This educational content guides students through analyzing variance (ANOVA) data to determine statistical significance and understand which treatments differ using Fisher's LSD method.
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