HW1: The Coffee Shop Mystery

A Statistical Investigation

Author

Dr. Marcela Alfaro Córdoba

🔍 The Case

Welcome, Statistical Detective!

You’ve been hired as a data consultant by Brew Haven, a local coffee shop chain with 5 locations around the city. The owner, Maria, has noticed something strange:

“Our downtown location seems to be struggling. Customers aren’t staying as long, satisfaction scores are lower, and we’re losing business to competitors. But I don’t know why! Is it the music? The seating? The staff? I need your help to figure this out using data and proper statistical methods.”

Maria has some theories but needs scientific evidence before making expensive changes. She’s willing to collect data, but she needs you to design the investigation and analyze the results.

Your mission: Use your statistical knowledge to help Maria solve this mystery and save Brew Haven’s downtown location!

Question 1: Define these terms in the context of Brew Haven

  1. Population:

  2. Sample:

  3. Parameter:

  4. Statistic:

Question 2: Sampling Strategy

Maria wants to survey customers across all 5 locations.

a. Choose and justify a sampling method

  • Which method: (Simple Random, Stratified, Systematic, Cluster, or Convenience)?
  • Why is this best for comparing locations?
  • How specifically would you implement it?

b. Identify bias

List THREE sources of bias and how to minimize each:

  1. Bias: _____________ | Solution:

  2. Bias: _____________ | Solution:

  3. Bias: _____________ | Solution:

Question 3: Design the Music Experiment

Maria thinks background music affects customer satisfaction and time spent in the shop.

a. Variables

  • Explanatory variable (include type):
  • Response variable (include type):
  • Two confounding variables to control:

b. Design

  • Control group:
  • Treatment group:
  • Random assignment process:

c. Ethics - List TWO ethical considerations:

Question 4: Classify Variables

For each variable, identify as quantitative (discrete/continuous) or qualitative (nominal/ordinal/binary):

Variable Classification Specific Type
Customer satisfaction (1-5 scale)
Type of drink ordered
Time spent in shop (minutes)
Number of items purchased
Location name
Amount spent ($)

Question 5: Time Spent Analysis

Downtown data (time in minutes for 25 customers): 12, 45, 28, 35, 15, 52, 8, 38, 42, 25, 18, 48, 32, 22, 40, 5, 35, 28, 45, 30, 20, 38, 15, 42, 25

a. Central tendency - Mean (show calculation): - Median: - Mode: - Write the formula for mean using sigma notation and calculate \(\sum x\):

b. Spread - Range: - Standard deviation (show work using \(s = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}\)): - Interpret: What does this tell Maria about customers?

c. Distribution - Create a frequency table:

Time Interval Frequency
0-15 min
16-30 min
31-45 min
46-60 min
  • Sketch a histogram
  • Five-number summary: Min_____ Q1_____ Median_____ Q3_____ Max_____
  • Shape: Symmetric, skewed left, or skewed right?
  • Interpretation: What does this shape tell Maria?

Question 6: Downtown vs. Midtown

Midtown data (time in minutes for 25 customers): 45, 52, 48, 55, 42, 50, 38, 58, 45, 48, 52, 40, 55, 48, 50, 45, 52, 48, 42, 50, 55, 48, 45, 52, 48

a. Calculate for Midtown - Mean (show work): - Median: - Standard deviation (show work):

b. Compare

Measure Downtown Midtown Interpretation
Mean
Median
Std Dev

c. Key findings - What’s the main difference in customer behavior? - What should Maria investigate next?

Question 7: Satisfaction Ratings

Maria shows you satisfaction rating patterns (1-5 scale) from three locations:

Location A: Most ratings 4-5, few lower ratings (tail to the left) Location B: Ratings evenly spread across 1-5 Location C: Most ratings 1-2, few higher ratings (tail to the right)

For each, identify: - Skewness (left, right, or symmetric) - Which is higher: mean or median? - One-sentence interpretation

Location A:

Location B:

Location C:

💭 Question 8: Detective’s Journal

Reflect on your investigation (5-7 sentences): - What statistical concepts were most crucial in solving this mystery? - What surprised you about the data? - How would you approach this differently if you could start over? - What real-world situations might require similar statistical investigations?

🎉 Good luck, Statistical Detective! Brew Haven is counting on you!