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:41 = 2 = 43: The average hourly rates are the same. %3D 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 10.75 11.75 13.5 11 10 13.75 13 11.25 17 8.75 12 14.75 14 14.75 16.75 Round all values including intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Cashiers Servers Cooks Grand Mean I; S The Sum of Squares within each group SS, = (z- 2.) %3D One Way Analysis of Variance (ANOVA) ANOVA Table
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:41 = 2 = 43: The average hourly rates are the same. %3D 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 10.75 11.75 13.5 11 10 13.75 13 11.25 17 8.75 12 14.75 14 14.75 16.75 Round all values including intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Cashiers Servers Cooks Grand Mean I; S The Sum of Squares within each group SS, = (z- 2.) %3D One Way Analysis of Variance (ANOVA) ANOVA Table
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Educational Content on Analysis of Variance (ANOVA)**
---
**Objective:**
You are conducting an Analysis of Variance (ANOVA) to determine if there is a difference 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 across all groups.
- \( H_a: \) At least one average hourly rate is different from the others (claim).
**Significance Level:**
- \(\alpha = 0.025\)
**Data Table:**
- **Group 1: Cashiers**
- 10.75, 11, 13, 8.75, 14
- **Group 2: Servers**
- 11.75, 10, 11.25, 12, 14.75
- **Group 3: Cooks**
- 13.5, 13.75, 17, 14.75, 16.75
**Instructions:**
Round all calculated values, including intermediate steps, to two decimal places. Fill in the summary table for the means, grand mean, and sum of squares.
**Summary Table:**
| | Cashiers | Servers | Cooks | Grand \(\bar{x}\) |
|-------|----------|---------|-------|------------------|
| Mean \(\bar{x}_i\) | | | | |
| \(SS_i\) (Sum of Squares)| | | | |
**Sum of Squares Formula:**
The sum of squares within each group is calculated as:
\[ SS_i = \sum (x - \bar{x}_i)^2 \]
**ANOVA Table:**
To calculate the ANOVA, you'll need these values and further calculations regarding between-group and within-group variabilities.
This example demonstrates how to set up and analyze data using ANOVA to find potential differences in group means, which can be crucial for decision-making in business environments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafbb34f7-6cc7-4027-b1ef-aba15d7abbe8%2F34971a4b-0c6f-43a9-9672-260d9475046d%2Fi4pbgd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Analysis of Variance (ANOVA)**
---
**Objective:**
You are conducting an Analysis of Variance (ANOVA) to determine if there is a difference 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 across all groups.
- \( H_a: \) At least one average hourly rate is different from the others (claim).
**Significance Level:**
- \(\alpha = 0.025\)
**Data Table:**
- **Group 1: Cashiers**
- 10.75, 11, 13, 8.75, 14
- **Group 2: Servers**
- 11.75, 10, 11.25, 12, 14.75
- **Group 3: Cooks**
- 13.5, 13.75, 17, 14.75, 16.75
**Instructions:**
Round all calculated values, including intermediate steps, to two decimal places. Fill in the summary table for the means, grand mean, and sum of squares.
**Summary Table:**
| | Cashiers | Servers | Cooks | Grand \(\bar{x}\) |
|-------|----------|---------|-------|------------------|
| Mean \(\bar{x}_i\) | | | | |
| \(SS_i\) (Sum of Squares)| | | | |
**Sum of Squares Formula:**
The sum of squares within each group is calculated as:
\[ SS_i = \sum (x - \bar{x}_i)^2 \]
**ANOVA Table:**
To calculate the ANOVA, you'll need these values and further calculations regarding between-group and within-group variabilities.
This example demonstrates how to set up and analyze data using ANOVA to find potential differences in group means, which can be crucial for decision-making in business environments.
![**ANOVA Table**
| | Sum of Squares (SS) | Degrees of Freedom (df) | Mean of Squares (MS) | F-Test Statistic |
|---------------------------|-----------------------------|-------------------------------------------------|----------------------------------|-------------------------------|
| **Between (Numerator)** | \( SS_B = \sum n_i (\bar{x}_i - \bar{x})^2 \) | \( df_B = df_1 = k - 1 \) | \( MS_B = \frac{SS_B}{df_B} \) | \( F = \frac{MS_B}{MS_W} \) |
| **Within (Denominator)** | \( SS_W = \sum SS_i = \sum \sum (x - \bar{x}_i)^2 \) | \( df_W = df_2 = N - k \) | \( MS_W = \frac{SS_W}{df_W} \) | |
| **Total** | \( SS_T = SS_B + SS_W \) | \( df_T = df_B + df_W \) | | |
**Definitions**
- \( \bar{x}_i \): Mean of each group
- \( \bar{x} \): Grand Mean (Mean of all data points)
- \( SS_B \): Sum of Squares between groups
- \( SS_W \): Sum of Squares within each group
- \( df_B \): Degrees of Freedom between groups
- \( df_W \): Degrees of Freedom within each group
- \( N \): Total number of data points in all groups
- \( k \): Number of groups
- \( MS_B \): Mean of the Squares between groups
- \( MS_W \): Mean of the Squares within each group
**Summary Table for ANOVA Test**
| | SS | df | MS | F |
|-----------|-----|-----|-----|----|
| **Between**| | | | |
| **Within** | | | | |
| **Total** | | | | |
**Critical Value** \( F_0 = \) [Blank for input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafbb34f7-6cc7-4027-b1ef-aba15d7abbe8%2F34971a4b-0c6f-43a9-9672-260d9475046d%2F7f91t0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**ANOVA Table**
| | Sum of Squares (SS) | Degrees of Freedom (df) | Mean of Squares (MS) | F-Test Statistic |
|---------------------------|-----------------------------|-------------------------------------------------|----------------------------------|-------------------------------|
| **Between (Numerator)** | \( SS_B = \sum n_i (\bar{x}_i - \bar{x})^2 \) | \( df_B = df_1 = k - 1 \) | \( MS_B = \frac{SS_B}{df_B} \) | \( F = \frac{MS_B}{MS_W} \) |
| **Within (Denominator)** | \( SS_W = \sum SS_i = \sum \sum (x - \bar{x}_i)^2 \) | \( df_W = df_2 = N - k \) | \( MS_W = \frac{SS_W}{df_W} \) | |
| **Total** | \( SS_T = SS_B + SS_W \) | \( df_T = df_B + df_W \) | | |
**Definitions**
- \( \bar{x}_i \): Mean of each group
- \( \bar{x} \): Grand Mean (Mean of all data points)
- \( SS_B \): Sum of Squares between groups
- \( SS_W \): Sum of Squares within each group
- \( df_B \): Degrees of Freedom between groups
- \( df_W \): Degrees of Freedom within each group
- \( N \): Total number of data points in all groups
- \( k \): Number of groups
- \( MS_B \): Mean of the Squares between groups
- \( MS_W \): Mean of the Squares within each group
**Summary Table for ANOVA Test**
| | SS | df | MS | F |
|-----------|-----|-----|-----|----|
| **Between**| | | | |
| **Within** | | | | |
| **Total** | | | | |
**Critical Value** \( F_0 = \) [Blank for input]
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