[Solved] MAT MILESTONE5

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**files (2)**

– ## MAT202YourPaceMilestone511.docx

– MAT_202_YourPace_Milestone_5_Data.xlsx

**## MAT202YourPaceMilestone511.docx**

## Milestone 5

**F-Distribution Comprehensive Assessment**

**Regional Restaurant Chain Quality Analysis**

**Scenario: Fresh Eats Restaurant Chain**

Fresh Eats is a regional restaurant chain with locations across four different market areas: Urban Metro, Suburban Communities, College Towns, and Rural Areas. The corporate office is conducting a comprehensive analysis to evaluate operational consistency and service quality across all locations. As the lead data analyst, you must use F-distribution statistical methods to provide insights that will guide strategic decisions.

The company has collected data from 120 restaurants (30 from each market type) measuring key performance indicators.

**Dataset:** Use the provided ‘MAT 202 YourPace Final Assessment Data’ file for all analyses.

·
**Market_Area:** Restaurant location type (Urban_Metro, Suburban, College_Town, Rural)

·
**Customer_Satisfaction:** Overall satisfaction rating (1-10 scale)

·
**Service_Speed:** Average service time in minutes

·
**Food_Quality:** Food quality rating (1-10 scale)

·
**Staff_Friendliness:** Staff friendliness rating (1-10 scale)

**Submission:** Submit your Word document with all graphs, charts, and outputs and your .mpx Minitab file.

**Part A: F-Distribution Properties and Sample Size Effects**

**A1. Distribution Shape Analysis** Create F-distribution plots for scenarios representing different sample sizes:

· Small samples: F(3,20)

· Medium samples: F(3,40)

· Large samples: F(3,116) (your actual data)

**Interpretation Questions:**

1.
**Shape Comparison:** Based on your F-distribution plots, which scenario (small, medium, or large sample) has:

· The highest peak? _____

· The most right-skewed distribution? _____

· The distribution most similar to normal? _____

2.
**Critical Value Analysis:** Calculate and record the critical values (α = 0.05):

· F₀.₀₅(3,20) = _____

· F₀.₀₅(3,40) = _____

· F₀.₀₅(3,116) = _____

**Interpretation:** If you calculated an F-statistic of 2.8 in each scenario, in which cases would you reject the null hypothesis?

Why does this pattern occur as sample size increases?

**Part B: One-Way ANOVA and Tukey's Test**

**B1. Customer Satisfaction Analysis** Conduct one-way ANOVA using Customer_Satisfaction as the response variable and Market_Area as the factor.

**Interpretation Questions:**

1.
**ANOVA Results:** Extract and record from your output:

· F-statistic =

· p-value =

· dftreatment =

· dferror = _____

**Decision:** With α = 0.05, do you reject or fail to reject H₀?

What does this tell you about customer satisfaction across market areas?

2.
**Tukey's Results:** Complete the significance table based on your output:

| | | | |
| — | — | — | — |
| **Comparison** | **Mean Difference** | **p-value** | **Significant (Y/N)?** |
| Suburban vs Urban_Metro | | | |
| Suburban vs College_Town | | | |
| Urban_Metro vs College_Town | | | |

**Ranking:** List the market areas from highest to lowest customer satisfaction:

1st:

2nd:

3rd:

4th:

3.
**Business Impact:** Which market area should Fresh Eats prioritize for customer satisfaction improvements?

Which market area appears to be the performance benchmark? _____

**B2. Service Speed Comparison**

4.
**Comparative Results:**

· Service Speed F-statistic =

· p-value =

· Customer Satisfaction F-statistic =

· p-value = _____

**Interpretation:** Which performance measure shows stronger evidence of differences between market areas?

What does this suggest about where Fresh Eats should focus improvement efforts?

**Part C: Two-Variance Testing**

**C1. Variance Equality Analysis** Conduct a 2-sample variance test comparing Food_Quality variance between Urban Metro and Suburban markets.

**Interpretation Questions:**

1.
**Test Setup:** Record your hypotheses:

· H₀: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

· H₁: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

2.
**Test Results:** Extract from your output:

· F-statistic =

· p-value =

· 95% confidence interval for variance ratio:

3.
**Statistical Decision:** With α = 0.05, do you reject or fail to reject H₀?

4.
**Confidence Interval Interpretation:**

· Does your confidence interval contain 1.0?

· What does this tell you about variance equality?

5.
**Business Interpretation:**

· Which market type has more consistent food quality: Urban Metro or Suburban?

· What are the implications for standardization efforts?

· Should Fresh Eats investigate why one market area is less consistent?

**Part D: Integrated Analysis and Statistical Communication**

**D1. Results Integration**

1.
**Test Summary:** Complete your results table:

| | | | |
| — | — | — | — |
| **Analysis** | **F-Statistic** | **p-value** | **Conclusion** |
| Customer Satisfaction ANOVA | | | |
| Service Speed ANOVA | | | |
| Food Quality Variance Test | | | |

2.
**Pattern Recognition:** Which analysis provided the strongest evidence of market area differences?

Which provided the weakest evidence? _____

**D2. Business Decision Making**

3.
**Priority Assessment:** Based on your statistical results:

· Which market area needs the most immediate attention?

· Which performance area (customer satisfaction, service speed, or food quality) should be the top priority?

· Which market area could serve as a best-practice model?

4.
**Statistical vs. Practical Significance:**

· Even if differences are statistically significant, are they large enough to justify different management strategies?

· What is the largest mean difference you found between market areas?

· Is this difference meaningful from a business perspective?

**MAT_202_YourPace_Milestone_5_Data.xlsx**

This file is too large to display. [View in new window](https://www.sweetstudy.com/files/mat-202-yourpace-milestone-5-data-xlsx)

**MAT_202_YourPace_Milestone_5_Data.xlsx**

This file is too large to display. [View in new window](https://www.sweetstudy.com/files/mat-202-yourpace-milestone-5-data-xlsx)

**## MAT202YourPaceMilestone511.docx**

## Milestone 5

**F-Distribution Comprehensive Assessment**

**Regional Restaurant Chain Quality Analysis**

**Scenario: Fresh Eats Restaurant Chain**

Fresh Eats is a regional restaurant chain with locations across four different market areas: Urban Metro, Suburban Communities, College Towns, and Rural Areas. The corporate office is conducting a comprehensive analysis to evaluate operational consistency and service quality across all locations. As the lead data analyst, you must use F-distribution statistical methods to provide insights that will guide strategic decisions.

The company has collected data from 120 restaurants (30 from each market type) measuring key performance indicators.

**Dataset:** Use the provided ‘MAT 202 YourPace Final Assessment Data’ file for all analyses.

·
**Market_Area:** Restaurant location type (Urban_Metro, Suburban, College_Town, Rural)

·
**Customer_Satisfaction:** Overall satisfaction rating (1-10 scale)

·
**Service_Speed:** Average service time in minutes

·
**Food_Quality:** Food quality rating (1-10 scale)

·
**Staff_Friendliness:** Staff friendliness rating (1-10 scale)

**Submission:** Submit your Word document with all graphs, charts, and outputs and your .mpx Minitab file.

**Part A: F-Distribution Properties and Sample Size Effects**

**A1. Distribution Shape Analysis** Create F-distribution plots for scenarios representing different sample sizes:

· Small samples: F(3,20)

· Medium samples: F(3,40)

· Large samples: F(3,116) (your actual data)

**Interpretation Questions:**

1.
**Shape Comparison:** Based on your F-distribution plots, which scenario (small, medium, or large sample) has:

· The highest peak? _____

· The most right-skewed distribution? _____

· The distribution most similar to normal? _____

2.
**Critical Value Analysis:** Calculate and record the critical values (α = 0.05):

· F₀.₀₅(3,20) = _____

· F₀.₀₅(3,40) = _____

· F₀.₀₅(3,116) = _____

**Interpretation:** If you calculated an F-statistic of 2.8 in each scenario, in which cases would you reject the null hypothesis?

Why does this pattern occur as sample size increases?

**Part B: One-Way ANOVA and Tukey's Test**

**B1. Customer Satisfaction Analysis** Conduct one-way ANOVA using Customer_Satisfaction as the response variable and Market_Area as the factor.

**Interpretation Questions:**

1.
**ANOVA Results:** Extract and record from your output:

· F-statistic =

· p-value =

· dftreatment =

· dferror = _____

**Decision:** With α = 0.05, do you reject or fail to reject H₀?

What does this tell you about customer satisfaction across market areas?

2.
**Tukey's Results:** Complete the significance table based on your output:

| | | | |
| — | — | — | — |
| **Comparison** | **Mean Difference** | **p-value** | **Significant (Y/N)?** |
| Suburban vs Urban_Metro | | | |
| Suburban vs College_Town | | | |
| Urban_Metro vs College_Town | | | |

**Ranking:** List the market areas from highest to lowest customer satisfaction:

1st:

2nd:

3rd:

4th:

3.
**Business Impact:** Which market area should Fresh Eats prioritize for customer satisfaction improvements?

Which market area appears to be the performance benchmark? _____

**B2. Service Speed Comparison**

4.
**Comparative Results:**

· Service Speed F-statistic =

· p-value =

· Customer Satisfaction F-statistic =

· p-value = _____

**Interpretation:** Which performance measure shows stronger evidence of differences between market areas?

What does this suggest about where Fresh Eats should focus improvement efforts?

**Part C: Two-Variance Testing**

**C1. Variance Equality Analysis** Conduct a 2-sample variance test comparing Food_Quality variance between Urban Metro and Suburban markets.

**Interpretation Questions:**

1.
**Test Setup:** Record your hypotheses:

· H₀: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

· H₁: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

2.
**Test Results:** Extract from your output:

· F-statistic =

· p-value =

· 95% confidence interval for variance ratio:

3.
**Statistical Decision:** With α = 0.05, do you reject or fail to reject H₀?

4.
**Confidence Interval Interpretation:**

· Does your confidence interval contain 1.0?

· What does this tell you about variance equality?

5.
**Business Interpretation:**

· Which market type has more consistent food quality: Urban Metro or Suburban?

· What are the implications for standardization efforts?

· Should Fresh Eats investigate why one market area is less consistent?

**Part D: Integrated Analysis and Statistical Communication**

**D1. Results Integration**

1.
**Test Summary:** Complete your results table:

| | | | |
| — | — | — | — |
| **Analysis** | **F-Statistic** | **p-value** | **Conclusion** |
| Customer Satisfaction ANOVA | | | |
| Service Speed ANOVA | | | |
| Food Quality Variance Test | | | |

2.
**Pattern Recognition:** Which analysis provided the strongest evidence of market area differences?

Which provided the weakest evidence? _____

**D2. Business Decision Making**

3.
**Priority Assessment:** Based on your statistical results:

· Which market area needs the most immediate attention?

· Which performance area (customer satisfaction, service speed, or food quality) should be the top priority?

· Which market area could serve as a best-practice model?

4.
**Statistical vs. Practical Significance:**

· Even if differences are statistically significant, are they large enough to justify different management strategies?

· What is the largest mean difference you found between market areas?

· Is this difference meaningful from a business perspective?

**MAT_202_YourPace_Milestone_5_Data.xlsx**

This file is too large to display. [View in new window](https://www.sweetstudy.com/files/mat-202-yourpace-milestone-5-data-xlsx)

**## MAT202YourPaceMilestone511.docx**

## Milestone 5

**F-Distribution Comprehensive Assessment**

**Regional Restaurant Chain Quality Analysis**

**Scenario: Fresh Eats Restaurant Chain**

Fresh Eats is a regional restaurant chain with locations across four different market areas: Urban Metro, Suburban Communities, College Towns, and Rural Areas. The corporate office is conducting a comprehensive analysis to evaluate operational consistency and service quality across all locations. As the lead data analyst, you must use F-distribution statistical methods to provide insights that will guide strategic decisions.

The company has collected data from 120 restaurants (30 from each market type) measuring key performance indicators.

**Dataset:** Use the provided ‘MAT 202 YourPace Final Assessment Data’ file for all analyses.

·
**Market_Area:** Restaurant location type (Urban_Metro, Suburban, College_Town, Rural)

·
**Customer_Satisfaction:** Overall satisfaction rating (1-10 scale)

·
**Service_Speed:** Average service time in minutes

·
**Food_Quality:** Food quality rating (1-10 scale)

·
**Staff_Friendliness:** Staff friendliness rating (1-10 scale)

**Submission:** Submit your Word document with all graphs, charts, and outputs and your .mpx Minitab file.

**Part A: F-Distribution Properties and Sample Size Effects**

**A1. Distribution Shape Analysis** Create F-distribution plots for scenarios representing different sample sizes:

· Small samples: F(3,20)

· Medium samples: F(3,40)

· Large samples: F(3,116) (your actual data)

**Interpretation Questions:**

1.
**Shape Comparison:** Based on your F-distribution plots, which scenario (small, medium, or large sample) has:

· The highest peak? _____

· The most right-skewed distribution? _____

· The distribution most similar to normal? _____

2.
**Critical Value Analysis:** Calculate and record the critical values (α = 0.05):

· F₀.₀₅(3,20) = _____

· F₀.₀₅(3,40) = _____

· F₀.₀₅(3,116) = _____

**Interpretation:** If you calculated an F-statistic of 2.8 in each scenario, in which cases would you reject the null hypothesis?

Why does this pattern occur as sample size increases?

**Part B: One-Way ANOVA and Tukey's Test**

**B1. Customer Satisfaction Analysis** Conduct one-way ANOVA using Customer_Satisfaction as the response variable and Market_Area as the factor.

**Interpretation Questions:**

1.
**ANOVA Results:** Extract and record from your output:

· F-statistic =

· p-value =

· dftreatment =

· dferror = _____

**Decision:** With α = 0.05, do you reject or fail to reject H₀?

What does this tell you about customer satisfaction across market areas?

2.
**Tukey's Results:** Complete the significance table based on your output:

| | | | |
| — | — | — | — |
| **Comparison** | **Mean Difference** | **p-value** | **Significant (Y/N)?** |
| Suburban vs Urban_Metro | | | |
| Suburban vs College_Town | | | |
| Urban_Metro vs College_Town | | | |

**Ranking:** List the market areas from highest to lowest customer satisfaction:

1st:

2nd:

3rd:

4th:

3.
**Business Impact:** Which market area should Fresh Eats prioritize for customer satisfaction improvements?

Which market area appears to be the performance benchmark? _____

**B2. Service Speed Comparison**

4.
**Comparative Results:**

· Service Speed F-statistic =

· p-value =

· Customer Satisfaction F-statistic =

· p-value = _____

**Interpretation:** Which performance measure shows stronger evidence of differences between market areas?

What does this suggest about where Fresh Eats should focus improvement efforts?

**Part C: Two-Variance Testing**

**C1. Variance Equality Analysis** Conduct a 2-sample variance test comparing Food_Quality variance between Urban Metro and Suburban markets.

**Interpretation Questions:**

1.
**Test Setup:** Record your hypotheses:

· H₀: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

· H₁: σ²ᵤᵣᵦₐₙ _____ σ²ˢᵘᵇᵘʳᵇₐₙ

2.
**Test Results:** Extract from your output:

· F-statistic =

· p-value =

· 95% confidence interval for variance ratio:

3.
**Statistical Decision:** With α = 0.05, do you reject or fail to reject H₀?

4.
**Confidence Interval Interpretation:**

· Does your confidence interval contain 1.0?

· What does this tell you about variance equality?

5.
**Business Interpretation:**

· Which market type has more consistent food quality: Urban Metro or Suburban?

· What are the implications for standardization efforts?

· Should Fresh Eats investigate why one market area is less consistent?

**Part D: Integrated Analysis and Statistical Communication**

**D1. Results Integration**

1.
**Test Summary:** Complete your results table:

| | | | |
| — | — | — | — |
| **Analysis** | **F-Statistic** | **p-value** | **Conclusion** |
| Customer Satisfaction ANOVA | | | |
| Service Speed ANOVA | | | |
| Food Quality Variance Test | | | |

2.
**Pattern Recognition:** Which analysis provided the strongest evidence of market area differences?

Which provided the weakest evidence? _____

**D2. Business Decision Making**

3.
**Priority Assessment:** Based on your statistical results:

· Which market area needs the most immediate attention?

· Which performance area (customer satisfaction, service speed, or food quality) should be the top priority?

· Which market area could serve as a best-practice model?

4.
**Statistical vs. Practical Significance:**

· Even if differences are statistically significant, are they large enough to justify different management strategies?

· What is the largest mean difference you found between market areas?

· Is this difference meaningful from a business perspective?

**MAT_202_YourPace_Milestone_5_Data.xlsx**

This file is too large to display. [View in new window](https://www.sweetstudy.com/files/mat-202-yourpace-milestone-5-data-xlsx)