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	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	[   ,  ]

Answer 1

a1)

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

			Lower bound	Upper bound
	(xi-xj )	ME	(xi-xj)-ME	(xi-xj)+ME
Coke-new coke	41.50	30.22	11.28	71.72
Coke-Pepsi	30.20	30.22	-0.02	60.42
new coke-Pepsi	-11.30	30.22	-41.52	18.92