The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled. Use a = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Sum of Squares Degrees Mean Square F p-value Source of Variation (to whole number) of Freedom (to 2 decimals) (to 2 decimals) (to 4 decimals) X * X X Treatments Error Total The p-value is less than 0.01 What is your conclusion? Conclude not all treatment means are equal v S X X * * Italian $ 11 $ 12 $ 13 $16 $ 19 $ 20 $18 $ 24 Seafood $15 $18 $18 $24 $ 21 $ 13 $ 17 $18 Steakhouse $ 24 $18 $ 21 $25 $ 21 $21 $ 28 $ 30 4
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled. Use a = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Sum of Squares Degrees Mean Square F p-value Source of Variation (to whole number) of Freedom (to 2 decimals) (to 2 decimals) (to 4 decimals) X * X X Treatments Error Total The p-value is less than 0.01 What is your conclusion? Conclude not all treatment means are equal v S X X * * Italian $ 11 $ 12 $ 13 $16 $ 19 $ 20 $18 $ 24 Seafood $15 $18 $18 $24 $ 21 $ 13 $ 17 $18 Steakhouse $ 24 $18 $ 21 $25 $ 21 $21 $ 28 $ 30 4
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:**Analysis of Restaurant Meal Prices: ANOVA Study**
The **Consumer Reports** Restaurant Customer Satisfaction Survey collected data from **148,599 visits** to full-service restaurant chains. The study focuses on the average meal price (excluding tips) by category: Italian, Seafood, and Steakhouse. Data was sampled from 24 restaurants, categorized equally into three groups of 8.
### Data Overview
- **Italian Restaurants ($)**
- Prices: 11, 12, 13, 13, 19, 20, 18, 24
- **Seafood Restaurants ($)**
- Prices: 15, 18, 13, 18, 21, 13, 17, 18
- **Steakhouse ($)**
- Prices: 24, 18, 21, 25, 21, 31, 28, 30
### Purpose
To determine if there is a significant difference in mean meal prices among the three restaurant types using an alpha level of **0.05**.
### ANOVA Table Structure
- **Source of Variation**
- Treatments
- Error
- Total
- **Columns**
- Sum of Squares
- Degrees of Freedom
- Mean Square
- F-statistic
- p-value
### Results Interpretation
- The p-value is stated to be **less than 0.01**, indicating a significant difference in meal prices between the restaurant types.
- **Conclusion**: Since the p-value is less than the alpha level of 0.05, we reject the null hypothesis. Therefore, not all treatment means are equal, indicating significant differences in meal prices across restaurant types.
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