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 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 above given output:
test statistic F =6.57
p value =0.007
a-2)since p value <0.05
Reject H_{0}
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 | |||
(x_{i}-x_{j})-ME | (x_{i}-x_{j})+ME | |||
μ1-μ2 | 11.28 | 71.72 | ||
μ1-μ3 | -0.02 | 60.42 | ||
μ2-μ3 | -41.52 | 18.92 |
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