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 | 44 | 126 | 144 | 53 | 145 | 30 | 77 | 232 | 107 | 84 |
New Coke | 5 | 106 | 63 | 63 | 43 | 11 | 35 | 146 | 69 | 139 |
Pepsi | 27 | 94 | 102 | 41 | 58 | 47 | 69 | 130 | 68 | 104 |
Two-way ANOVA: Cans versus Drink, Building
Source | DF | SS | MS | F | P |
Drink | 2 | 9,206.6 | 4,603.30 | 6.57 | .007 |
Building | 9 | 54,523.6 | 6,058.18 | 8.64 | .000 |
Error | 18 | 12,614.1 | 700.78 | ||
Total | 29 | 76,344.3 | |||
Descriptive Statistics: Cans | ||
Variable | Drink | Mean |
Cans | Coke Classic | 104.2 |
New Coke | 62.7 | |
Pepsi | 74.0 | |
(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 H0
Do not reject H0
(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 above given output:
test statistic F =6.57
p value =0.007
a-2)since p value <0.05
Reject H0
b)
MSE= | 700.7800 | ||
df(error)= | 18 | ||
number of treatments = | 3 | ||
pooled standard deviation=Sp =√MSE= | 26.472 |
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) = | 30.220 |
Confidence interval =sample mean difference -/+ HSD
Lower bound | Upper bound | |||
(xi-xj)-ME | (xi-xj)+ME | |||
μ1-μ2 | 11.28 | 71.72 | ||
μ1-μ3 | -0.02 | 60.42 | ||
μ2-μ3 | -41.52 | 18.92 |
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