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The ANOVA summary table for an experiment with four groups, with five values in each group, is shown to the right. Complete parts (a) through (d) below.

The ANOVA summary table for an experiment with four groups, with five values in each group, is shown to the right. Complete parts (a) through (d) below.

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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please calculate the test statistic please calculate the critical value Is there sufficient evidence. at the 0.05 level of significance, what is the upper-tail critical value from Studentized range distribution? at the 0.01 level of significance, what is the upper-tail critical value from Studentized range distribution? To perform the Tukey-Kramer procedure, what is the critical range?
## ANOVA Summary Table and Hypothesis Testing This section covers an ANOVA summary table for an experiment with four groups, each with five values. It explains how to determine if all groups have equal population means. ### ANOVA Summary Table The table below summarizes the analysis of variance (ANOVA) for the experiment: | Source | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F | |----------------|--------------------|----------------|------------------------|----------| | Among groups | c - 1 = 3 | SSA = 90 | MSA = 30 | | | Within groups | n - c = 16 | SSW = 160 | MSW = 10 | | | Total | n - 1 = 19 | SST = 250 | | F_stat = 3.00 | - **Among groups**: Measures variance between group means. - **Within groups**: Measures variance within each group. - **Total**: Total variance in the data. ### Hypothesis Testing - **Significance Level**: 0.05 - **Decision Rule**: Test if all four groups have equal population means. #### Hypotheses: Choose the correct hypothesis from the options: - **Option A**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_5 \) - \( H_1: \mu_1 \neq \mu_2 \neq \cdots \neq \mu_5 \) - **Option B**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_5 \) - \( H_1: \text{Not all the means are equal.} \) - **Option C**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_4 \) - \( H_1: \mu_1 \neq \mu_2 \neq \cdots \neq \mu_4 \) - **Option D (Correct)**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_4 \) - \( H_1: \text{Not all the means are equal.} \
Transcribed Image Text:## ANOVA Summary Table and Hypothesis Testing This section covers an ANOVA summary table for an experiment with four groups, each with five values. It explains how to determine if all groups have equal population means. ### ANOVA Summary Table The table below summarizes the analysis of variance (ANOVA) for the experiment: | Source | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F | |----------------|--------------------|----------------|------------------------|----------| | Among groups | c - 1 = 3 | SSA = 90 | MSA = 30 | | | Within groups | n - c = 16 | SSW = 160 | MSW = 10 | | | Total | n - 1 = 19 | SST = 250 | | F_stat = 3.00 | - **Among groups**: Measures variance between group means. - **Within groups**: Measures variance within each group. - **Total**: Total variance in the data. ### Hypothesis Testing - **Significance Level**: 0.05 - **Decision Rule**: Test if all four groups have equal population means. #### Hypotheses: Choose the correct hypothesis from the options: - **Option A**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_5 \) - \( H_1: \mu_1 \neq \mu_2 \neq \cdots \neq \mu_5 \) - **Option B**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_5 \) - \( H_1: \text{Not all the means are equal.} \) - **Option C**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_4 \) - \( H_1: \mu_1 \neq \mu_2 \neq \cdots \neq \mu_4 \) - **Option D (Correct)**: - \( H_0: \mu_1 = \mu_2 = \cdots = \mu_4 \) - \( H_1: \text{Not all the means are equal.} \
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