Some people like to pour beer gently down the side of the glass to preserve bubbles. Others, splash it down the center to release the bubbles into a foamy head and free the aromas. Champagne, however is best when the bubbles remain concentrated in the wine. According to an article in the Journal of Agricultural and hood Chemistry, a group of French scientists recently verified the difference between the two pouring methods by measuring the amount of bubbles in each glass of champagne poured two different ways and at three different temperatures (Journal of Agricultural and hood Chemistry, 2010). The following data present the pattern of results obtained in the study.
Champagne Temperature (°F)
40- | 46° | 52° | |
n = 10 | n = 10 | n = 10 | |
Gentle Pour | M = 7 | M = 3 | M = 2 |
SS= 64 | SS = 57 | SS = 47 | |
n = 10 | n = 10 | n = 10 | |
Splashing Pour | M = 5 | M = 1 | M = 0 |
SS = 56 | SS = 54 | SS =46 |
a. Use a two-factor ANOVA with α = .05 to evaluate the mean differences.
b. Briefly explain how temperature and pouring influence the bubbles in champagne according to this pattern of results.
a.
To find: The significance of mean difference using Two-factor ANOVA with
Given info:
The data with appropriate values is given inthe question.
Calculation:
Step 1: Hypothesis
Main effect hypothesis are:
For temperature:
For pouring influence:
Interaction hypothesis is:
Step 2:
First stage analysis :
And,
Similarly,
Second stage analysis:
Similarly,
And,
Now,
Step 3: Compute F-ratio
First,
And,
b.
To explain: The results of ANOVA
Essentials Of Statistics
Understanding Basic Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Contemporary Mathematics for Business & Consumers
Finite Mathematics
Calculus: Early Transcendental Functions (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Single Variable Calculus: Early Transcendentals
Finite Mathematics for the Managerial, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Applied Calculus
Elementary Technical Mathematics
Mathematical Applications for the Management, Life, and Social Sciences
Single Variable Calculus
Elementary Geometry For College Students, 7e
Calculus of a Single Variable
Intermediate Algebra
Calculus (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendentals
Elements Of Modern Algebra
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus: An Applied Approach (MindTap Course List)
Trigonometry (MindTap Course List)
Multivariable Calculus
Introduction To Statistics And Data Analysis
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Elementary Geometry for College Students
Study Guide for Stewart's Multivariable Calculus, 8th