The Coca-Cola Company introduced New Coke in 1985. Within three months of this introduction, negative consumer reaction forced Coca-Cola to reintroduce the original formula of Coke as Coca-Cola Classic. Suppose that two years later, in 1987, a marketing research firm in Chicago compared the sales of Coca-Cola Classic, New Coke, and Pepsi in public building vending machines. To do this, the marketing research firm randomly selected 10 public buildings in Chicago having both a Coke machine (selling Coke Classic and New Coke) and a Pepsi machine.
The Coca-Cola Data and a MINITAB Output of a Randomized Block ANOVA of the Data:
Building | ||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
Coke Classic | 38 | 139 | 123 | 53 | 136 | 32 | 69 | 230 | 120 | 83 |
New Coke | 10 | 105 | 60 | 60 | 44 | 10 | 38 | 155 | 69 | 134 |
Pepsi | 21 | 80 | 103 | 42 | 50 | 49 | 69 | 115 | 78 | 102 |
Two-way ANOVA: Cans versus Drink, Building
Source | DF | SS | MS | F | P |
Drink | 2 | 8,425.9 | 4,212.93 | 5.82 | .011 |
Building | 9 | 52,324.3 | 5,813.81 | 8.03 | .000 |
Error | 18 | 13,030.8 | 723.93 | ||
Total | 29 | 73,781.0 | |||
Descriptive Statistics: Cans | ||
Variable | Drink | Mean |
Cans | Coke Classic | 102.3 |
New Coke | 63.7 | |
Pepsi | 70.9 | |
(a-1) Calculate the value of the test statistic and p-value. (Round "test statistic" value to 2 decimal places and "p-value" to 3 decimal places.)
Test statistic | |
p-value | |
(a-2) At the 0.05 significance level, what is the conclusion?
Reject H_{0}
Do not reject H_{0}
(b) What is the Tukey simultaneous 95 percent confidence interval for the following? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
Confidence interval | |
Coke Classic - New Coke | [ , ] |
Coke Classic – Pepsi | [ , ] |
New Coke – Pepsi | [ , ] |
a-1)
from given output ANOVA table:
value of test statistic F =5.82
p value =0.011
a-2)
since p value <0.05
reject Ho
b)
MSE= | 723.930 | ||
df(error)= | 18 | ||
number of treatments = | 3 | ||
pooled standard deviation=Sp =√MSE= | 26.906 |
critical q with 0.05 level and k=3, N-k=18 df= | 3.61 | ||
Tukey's (HSD) =(q/√2)*(sp*√(1/ni+1/nj) = | 30.715 |
Lower bound | Upper bound | |||
(x_{i}-x_{j} ) | ME | (x_{i}-x_{j})-ME | (x_{i}-x_{j})+ME | |
Coke Classic-New Coke | 38.60 | 30.72 | 7.88 | 69.32 |
Coke Classic -Pepsi | 31.40 | 30.72 | 0.68 | 62.12 |
New Coke - Pepsi | -7.20 | 30.72 | -37.92 | 23.52 |
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