Question

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 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.)

Answer 1

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