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	38	139	123	53	136	32	69	230	120	83
New Coke	10	105	60	60	44	10	38	155	69	134
Pepsi	21	80	103	42	50	49	69	115	78	102

Two-way ANOVA: Cans versus Drink, Building

Source	DF	SS	MS	F	P
Drink	2	8,425.9	4,212.93	5.82	.011
Building	9	52,324.3	5,813.81	8.03	.000
Error	18	13,030.8	723.93
Total	29	73,781.0

Descriptive Statistics: Cans
Variable	Drink	Mean
Cans	Coke Classic	102.3
	New Coke	63.7
	Pepsi	70.9

(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

a-1)

from given output ANOVA table:

value of test statistic F =5.82

p value =0.011

a-2)

since p value <0.05

reject Ho

b)

MSE=			723.930
df(error)=			18
number of treatments =			3
pooled standard deviation=Sp =√MSE=			26.906

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)         =			30.715

			Lower bound	Upper bound
	(xi-xj )	ME	(xi-xj)-ME	(xi-xj)+ME
Coke Classic-New Coke	38.60	30.72	7.88	69.32
Coke Classic -Pepsi	31.40	30.72	0.68	62.12
New Coke - Pepsi	-7.20	30.72	-37.92	23.52