Question

 

A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table.

Bottle Design Study Data
A			B			C
	17			31			25
	16			35			20
	18			35			27
	19			31			22
	13			33			26

  

You will need to enter the data into Minitab. It is easiest to copy from here into Excel. Then copy and paste from Excel into Minitab. Besure that row 1 (the first white row in the spreadsheet) contains the first piece of data and that variable names are in the top grey row in Minitab.

  

(a)	Test the null hypothesis that μA, μB, and μC are equal by setting α = .05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

F
p-value

(Click to select)  Reject  Do not reject   H0: bottle design  (Click to select)  does not  does  have an impact on sales.

(b)	Based on Tukey's results, which bottle design maximizes mean daily sales?

Bottle design  (Click to select)  B  A  C   maximizes sales.

Answer 1

a)

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	674.533	2	337.27	56.84	0.0000
Within Groups	71.200	12	5.93
Total	745.733	14

F = 56.84

p value = 0.000

Reject H0: bottle design does have an impact on sales.

b)

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	12
MSE =	5.9333
q-statistic value(α,k,N-k)	3.7728

critical value = q*√(MSE/2*(1/ni+1/nj))

population mean difference	critical value			result
µ1-µ2	16.40	4.11			means are different
µ1-µ3	7.400	4.11			means are different
µ2-µ3	9.00	4.11			means are different

B   maximizes sales.