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 | 45 | 136 | 134 | 41 | 146 | 33 | 71 | 224 | 111 | 87 |
New Coke | 6 | 114 | 56 | 14 | 39 | 20 | 42 | 156 | 61 | 140 |
Pepsi | 24 | 90 | 100 | 43 | 51 | 42 | 68 | 131 | 74 | 107 |
Two-way ANOVA: Cans versus Drink, Building
Source | DF | SS | MS | F | P |
Drink | 2 | 7997.6 | 3998.80 | 5.78 | 0.011 |
Building | 9 | 55573.5 | 6174.83 | 8.93 | 0.000 |
Error | 18 | 12443.7 | 691.32 | ||
Total | 29 | 76014.8 | |||
Descriptive Statistics: Cans | ||
Variable | Drink | Mean |
Cans | Coke Classic | 102.8 |
New Coke | 64.8 | |
Pepsi | 73.0 | |
(a-1) Calculate the value of the test statistic and p-value. (Round "test statistic" value to 2 decimal places and "p-value" to 4 decimal places.)
(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.)
a1)
F stat = 5.78
p value= 0.011
a2)
p value= 0.011 <α=0.05, reject Ho
Reject H0
b)
Level of significance | 0.05 |
no. of treatments,k | 3 |
DF error =N-k= | 18 |
MSE | 691.32 |
q-statistic value(α,k,N-k) | 3.6093 |
critical value = q*√(MSE/n) = 30.01
confidence interval = mean difference ± critical value
confidence interval | |||||||
population mean difference | critical value | lower limit | upper limit | result | |||
µ1-µ2 | 38.00 | 30.01 | 7.99 | 68.01 | means are different | ||
µ1-µ3 | 29.800 | 30.01 | -0.21 | 59.81 | means are not different | ||
µ2-µ3 | -8.20 | 30.01 | -38.21 | 21.81 | means are not different |
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