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Statistical Inference Project, Company, Client - Coggle Diagram
Statistical Inference Project
Hillerd's Marketing
Market research and analysis company
Mendham Vending Manager
Runs vending machines in lunch areas
Question: Wants to understand drink preferences by age group
Goal: put the right drinks in the right lunch locations to increase sales and revenues
Project Topic
Drink preference by age/grade level
Compare preference for Coke products, Pepsi products, and other drinks
Use results to design vending machine product mixes at each lunch location (Big gym, small gym, Cafeteria, Lobby, Teacher's Lounge)
Research Question
Is there an association between grade level and preferred drink type?
Hypotheses
H0: Grade level and drink preference are independent (The distribution of Coke/Pepsi/Other is the same for all grades and teachers)
H1: Grade level and drink preference are not independent (There is an association between age/grade and preferred drink type, vending machine distribution will be different for each location)
α = 0.05
Data
Data collection
Population
All students and teachers at Mendham High School
20 Freshman
20 Sophomores
20 Juniors
20 Seniors
20 Teachers
100 total responses
Methods
Short survey with 2 questions:
What grade level are you in? (didn't ask to teachers, obviously)
What drink do you prefer?
Observed Data
Coke
Se: 9, J: 6, So:11, F:7, T:10
Pepsi
Se: 5, J: 7, So: 5, F: 10, T: 5
Other
Se: 6, J: 7, So: 4, F: 3, T: 5
Variables
Grade Level
Freshman
Sophomore
Junior
Senior
Teacher
Drink Preference
Coke products
Pepsi products
Other drinks (water, juice, sports drinks, etc.)
Calculations
Statistical Test
Why?
Two categorical variables (grade level and drink preference)
Goal
Test for association vs. independence
Chosen test
Chi- Squared Test for Independence
Results
Calculations
χ² ≈ 7.00
• p ≈ 0.54
• df = 8
Decision
p > 0.05 → fail to reject H0
Degrees of Freedom
(3-1)(5-1) = 2 x 4 = 8
Expected counts
Use formula: (row total × column total) / grand total
• Coke in each grade: (43 × 20) / 100 = 8.6
• Pepsi in each grade: (32 × 20) / 100 = 6.4
• Other in each grade: (25 × 20) / 100 = 5.0
Unit 5 Correlation
Goal
Analyze relationship using a correlation approach with coded ranks
Coding
• Grade codes: 1–5 (Freshman to Teacher)
• Drink codes: 1–3 (Other, Pepsi, Coke)
Results
Correlation r ≈ 0 (slightly negative, around −0.02)
essentially no relationship between grade rank and drink rank
Company
Client