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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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 determine

To find: The significance of mean difference using Two-factor ANOVA with α=0.05

Explanation

Given info:

The data with appropriate values is given inthe question.

Calculation:

Step 1: Hypothesis

Main effect hypothesis are:

For temperature:

H0: There is no temperature effect.

H1: There is a temperature effect.

For pouring influence:

H0: There is no pouring influence effect.

H1: There is a pouring influence effect.

Interaction hypothesis is:

H0: There is no interaction effect between temperature and pouring influence.

H1: There is an interaction effect between temperature and pouring influence.

Step 2:

First stage analysis :

dfwithin=5+5+5+5=20

And,

dftotal=N1

Similarly,

dfbetween=number_of_treatment1=41=3

Second stage analysis:

SSA=T2rownrowG2N=120230+60230180260=60

Similarly,

SSA=T2columnncolumnG2N=120220+40220+20220180260=280

And,

SA×B=SSbetween_treatmentSSASSB=34060280=0

Now,

Step 3: Compute F-ratio

First,

SStotal=X2G2N=35460215=114

And,

b.

To determine

To explain: The results of ANOVA

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