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You are running an Analysis of Variance to test if there is a difference in hourly rates of three types of restaurant workers': Cashiers, Servers and Cooks. Ho:#1 2 =3: The average hourly rates are the same. Ha: At least one average hourly rate is different from the others.(claim) a = 0,025 (Group 1) Cashiers (Group 2) Servers (Group 3) Cooks 14 9. 14.25 10.75 10.25 14 12.75 9.25 12 9.5 12.25 12.5 14 13.25 14 Round all values including all intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Servers Cooks Grand Cashiers Mean ; S Fill in the summary table for the ANOVA test:

You are running an Analysis of Variance to test if there is a difference in hourly rates of three types of restaurant workers': Cashiers, Servers and Cooks. Ho:#1 2 =3: The average hourly rates are the same. Ha: At least one average hourly rate is different from the others.(claim) a = 0,025 (Group 1) Cashiers (Group 2) Servers (Group 3) Cooks 14 9. 14.25 10.75 10.25 14 12.75 9.25 12 9.5 12.25 12.5 14 13.25 14 Round all values including all intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Servers Cooks Grand Cashiers Mean ; S Fill in the summary table for the ANOVA test:

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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### Educational Website Content: ANOVA Analysis **Text Instructions:** Round all values, including all intermediate calculations, to 2 decimal places. **Instructions for the First Table:** Fill in the summary table for the means, grand mean, and sum of squares (\( SSi \)). | Role | Cashiers | Servers | Cooks | Grand \(\bar{x}\) | |------------|----------|---------|-------|-------------------| | Mean \(\bar{x}_i\) | | | | | | \( SSi \) | | | | | **Instructions for the ANOVA Test Summary Table:** Fill in the summary table for the ANOVA test: | Source | SS | df | MS | F | |----------|-----|----|-----|----| | Between | | | | | | Within | | | | | | Total | | | | | **Critical Value and Conclusion:** - **Critical Value \( F_0 \):** (round to 3 decimal places) - **Conclusion:** Select an answer (dropdown menu) By calculating and filling these tables, you'll be able to perform an ANOVA test, which helps to determine if there are statistically significant differences between the means of different groups. ### How to Approach the Task: 1. **Calculate Means:** Compute the mean for each role (Cashiers, Servers, Cooks) and the grand mean. 2. **Calculate Sum of Squares (\( SSi \)):** Calculate the sum of squares for each group. 3. **Fill the ANOVA Table:** - **SS (Sum of Squares):** Calculate for "Between", "Within", and "Total." - **df (Degrees of Freedom):** Determine for both "Between" and "Within" categories. - **MS (Mean Square):** Compute by dividing SS by df. - **F (F-ratio):** Compute using the formula \( F = \frac{MS_{Between}}{MS_{Within}} \). 4. **Determine Critical Value \( F_0 \)**: Use statistical tables or software to find the critical value based on the chosen significance level and degrees of freedom. 5. **Make a Conclusion:** Compare the calculated F value with the critical value to determine if the null hypothesis can be rejected. This
Transcribed Image Text:### Educational Website Content: ANOVA Analysis **Text Instructions:** Round all values, including all intermediate calculations, to 2 decimal places. **Instructions for the First Table:** Fill in the summary table for the means, grand mean, and sum of squares (\( SSi \)). | Role | Cashiers | Servers | Cooks | Grand \(\bar{x}\) | |------------|----------|---------|-------|-------------------| | Mean \(\bar{x}_i\) | | | | | | \( SSi \) | | | | | **Instructions for the ANOVA Test Summary Table:** Fill in the summary table for the ANOVA test: | Source | SS | df | MS | F | |----------|-----|----|-----|----| | Between | | | | | | Within | | | | | | Total | | | | | **Critical Value and Conclusion:** - **Critical Value \( F_0 \):** (round to 3 decimal places) - **Conclusion:** Select an answer (dropdown menu) By calculating and filling these tables, you'll be able to perform an ANOVA test, which helps to determine if there are statistically significant differences between the means of different groups. ### How to Approach the Task: 1. **Calculate Means:** Compute the mean for each role (Cashiers, Servers, Cooks) and the grand mean. 2. **Calculate Sum of Squares (\( SSi \)):** Calculate the sum of squares for each group. 3. **Fill the ANOVA Table:** - **SS (Sum of Squares):** Calculate for "Between", "Within", and "Total." - **df (Degrees of Freedom):** Determine for both "Between" and "Within" categories. - **MS (Mean Square):** Compute by dividing SS by df. - **F (F-ratio):** Compute using the formula \( F = \frac{MS_{Between}}{MS_{Within}} \). 4. **Determine Critical Value \( F_0 \)**: Use statistical tables or software to find the critical value based on the chosen significance level and degrees of freedom. 5. **Make a Conclusion:** Compare the calculated F value with the critical value to determine if the null hypothesis can be rejected. This
You are conducting an Analysis of Variance (ANOVA) to determine if there are differences in the hourly rates of three types of restaurant workers: Cashiers, Servers, and Cooks. **Hypotheses:** - \( H_0: \mu_1 = \mu_2 = \mu_3 \) : The average hourly rates are the same. - \( H_a \) : At least one average hourly rate is different from the others (claim). **Significance Level:** - \( \alpha = 0.025 \) **Hourly Rates Data Table:** | Group 1 (Cashiers) | Group 2 (Servers) | Group 3 (Cooks) | |--------------------|------------------|-----------------| | 14 | 9 | 14.25 | | 10.75 | 10.25 | 14 | | 12.75 | 9.25 | 12 | | 9.5 | 12.25 | 12.5 | | 14 | 13.25 | 14 | **Instructions:** 1. Round all values, including intermediate calculations, to 2 decimal places. 2. Fill in the summary table for the means, grand mean, and sum of squares (\(SS_i\)). **Summary Table for Means and Sum of Squares:** | | Cashiers | Servers | Cooks | Grand \(\bar{X}\) | |---------------|----------|---------|-------|----------------| | Mean \(\bar{X}_i\) | | | | | | \(SS_i\) | | | | | **ANOVA Test Summary Table:** | Source | SS | df | MS | F | |-------------|------|-----|------|-----| | Between | | | | | | Within | | | | | | Total | | | | | Fill in the above tables with calculated values to complete your analysis.
Transcribed Image Text:You are conducting an Analysis of Variance (ANOVA) to determine if there are differences in the hourly rates of three types of restaurant workers: Cashiers, Servers, and Cooks. **Hypotheses:** - \( H_0: \mu_1 = \mu_2 = \mu_3 \) : The average hourly rates are the same. - \( H_a \) : At least one average hourly rate is different from the others (claim). **Significance Level:** - \( \alpha = 0.025 \) **Hourly Rates Data Table:** | Group 1 (Cashiers) | Group 2 (Servers) | Group 3 (Cooks) | |--------------------|------------------|-----------------| | 14 | 9 | 14.25 | | 10.75 | 10.25 | 14 | | 12.75 | 9.25 | 12 | | 9.5 | 12.25 | 12.5 | | 14 | 13.25 | 14 | **Instructions:** 1. Round all values, including intermediate calculations, to 2 decimal places. 2. Fill in the summary table for the means, grand mean, and sum of squares (\(SS_i\)). **Summary Table for Means and Sum of Squares:** | | Cashiers | Servers | Cooks | Grand \(\bar{X}\) | |---------------|----------|---------|-------|----------------| | Mean \(\bar{X}_i\) | | | | | | \(SS_i\) | | | | | **ANOVA Test Summary Table:** | Source | SS | df | MS | F | |-------------|------|-----|------|-----| | Between | | | | | | Within | | | | | | Total | | | | | Fill in the above tables with calculated values to complete your analysis.
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