MAT FINAL

Final Assessment

Regional Restaurant Chain Quality Analysis

Scenario: Global Coffee Chain Quality Assessment

You are a data analyst for BrewMaster Global, a multinational coffee chain with over 500 locations across North America and Europe. The company is conducting a comprehensive quality assessment to improve customer satisfaction and operational efficiency. As part of this initiative, you have been provided with data from multiple sources including customer surveys, operational metrics, and quality control measurements.

The executive team needs your statistical analysis to make informed decisions about:

· Service quality improvements

· Regional expansion strategies

· Staff training programs

· Customer satisfaction initiatives

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

The dataset contains information from 100 coffee shops across different regions, with the following variables:

· Shop_ID: Unique identifier for each shop

· Region: North America (NA) or Europe (EU)

· Daily_Customers: Number of customers served per day

· Service_Time: Average service time in minutes

· Satisfaction_Score: Customer satisfaction rating (1-10 scale)

· Defect_Rate: Percentage of orders with defects

· Staff_Training: Training level (Basic, Standard, Advanced)

· Revenue: Daily revenue in USD

· Complaints: Number of customer complaints per day

· Wait_Time_Before: Average wait time before training program (minutes)

· Wait_Time_After: Average wait time after training program (minutes)

· Weekend_Revenue: Weekend daily revenue

· Weekday_Revenue: Weekday daily revenue

· Customer_Return: Whether customer returned within 30 days (Yes/No)

· Premium_Orders: Number of premium coffee orders per day

· Regular_Orders: Number of regular coffee orders per day

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

Assessment Questions

Part A: Discrete Probability Distributions

Part 1A: The number of customer complaints per day follows a Poisson distribution. Using the Complaints variable:

a) Calculate the mean number of complaints per day across all shops.

b) What is the probability that a randomly selected shop receives exactly 3 complaints in a day?

c) What is the probability that a shop receives more than 5 complaints in a day?

d) The company considers a shop to have "excessive complaints" if it receives 7 or more complaints per day. What percentage of shops would be classified as having excessive complaints?

Part 2A: The company tracks premium coffee orders, which follow a binomial distribution. Assume each customer has a 0.3 probability of ordering a premium coffee.

a) For shops serving 50 customers per day, what is the expected number of premium orders?

b) What is the probability that exactly 18 out of 50 customers order premium coffee?

c) What is the probability that at least 20 customers order premium coffee?

d) Within what range would you expect 95% of premium orders to fall?

Part B: Continuous Probability Distributions

Part 1B: Service time follows a normal distribution. Using the Service_Time variable:

a) Calculate the mean and standard deviation of service time.

b) What percentage of orders are completed within 3 minutes?

c) The company wants to set a service time target such that 90% of orders are completed within this time. What should this target be?

d) If service time exceeds 3.5 minutes, customers receive a discount. What percentage of customers would receive this discount?

Part 2B: Customer satisfaction scores follow a normal distribution. Using the Satisfaction_Score variable:

a) Determine the mean and standard deviation of satisfaction scores.

b) What is the probability that a randomly selected customer gives a satisfaction score above 8?

c) The company wants to identify the bottom 10% of shops based on satisfaction scores for improvement programs. What is the cutoff satisfaction score?

d) What satisfaction score represents the 75th percentile?

Part C: Hypothesis Testing - Two Population Means

Part 1C: The company wants to compare average daily revenue between North American and European shops. Assume population standard deviations are known (σ₁ = $450, σ₂ = $380).

a) State the null and alternative hypotheses for testing if there's a difference in mean daily revenue between regions.

b) Conduct the appropriate hypothesis test at α = 0.05.

c) Calculate the 95% confidence interval for the difference in means.

d) Interpret your results in the business context.

Part 2C: Compare the average service time between North American and European shops, assuming population standard deviations are unknown.

a) State the null and alternative hypotheses.

b) Conduct the appropriate hypothesis test at α = 0.01.

c) Calculate the 99% confidence interval for the difference in means.

d) What conclusions can you draw about service time differences between regions?

Part 3C: The company implemented a staff training program and wants to evaluate its effectiveness by comparing wait times before and after training using the Wait_Time_Before and Wait_Time_After variables.

a) State the null and alternative hypotheses for this paired samples test.

b) Conduct the appropriate hypothesis test at α = 0.05.

c) Calculate the 95% confidence interval for the mean difference.

d) What is your conclusion about the training program's effectiveness?

Part D: Hypothesis Testing - Two Population Proportions

Part 1D: The company wants to compare customer return rates between North American and European shops using the Customer_Return variable.

a) Calculate the sample proportions of customers who return within 30 days for each region.

b) State the null and alternative hypotheses for testing if there's a difference in return rates.

c) Conduct the appropriate hypothesis test at α = 0.05.

d) Calculate the 95% confidence interval for the difference in proportions.

e) Interpret your findings and provide business recommendations.

Part E: Chi-Square Tests

Part 1E: Investigate whether there's a relationship between staff training level and customer satisfaction categories. Create satisfaction categories as Low (1-4.4), Medium (4.5-7.4), High (7.5-10).

a) Create a contingency table showing the relationship between training level and satisfaction categories.

b) State the null and alternative hypotheses for testing independence.

c) Conduct a chi-square test of independence at α = 0.05.

d) Interpret the results and discuss the practical implications.

Part F: F-Distribution and ANOVA

Part 1F: Test whether there are significant differences in mean daily revenue across the three staff training levels (Basic, Standard, Advanced).

a) State the null and alternative hypotheses.

b) Conduct a one-way ANOVA test at α = 0.05.

c) If significant differences exist, perform a Tukey test analysis to identify which groups differ.

d) Interpret your results and provide recommendations for the training program.