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

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**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.
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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