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
	19			30			25
	17			30			20
	18			33			22
	15			35			27
	18			29			21

The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

SUMMARY
Groups	Count	Sum	Average	Variance
Design A	5	87	17.4	2.3
Design B	5	157	31.4	6.3
Design C	5	115	23.0	8.5

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Between Groups	496.5333	2	248.2667	43.56	3.23E-06	3.88529
Within Groups	68.4	12.0	5.7000
Total	564.9333	14

(a) Test the null hypothesis that μ_A, μ_B, and μ_C 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)Do not rejectReject H₀: bottle design (Click to select)doesdoes not have an impact on sales.

(b) Consider the pairwise differences μ_B – μ_A, μ_C – μ_A , and μ_C – μ_B. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Point estimate Confidence interval

μB –μA: , [, ]

μC –μA: , [, ]

μC –μB: , [, ]

Bottle design (Click to select)CBA maximizes sales.

(c) Find a 95 percent confidence interval for each of the treatment means μ_A, μ_B, and μ_C. Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Confidence interval

μA: [, ]

μB: [, ]

μC: [, ]

Answer 1

Result:

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
	19			30			25
	17			30			20
	18			33			22
	15			35			27
	18			29			21

The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

SUMMARY
Groups	Count	Sum	Average	Variance
Design A	5	87	17.4	2.3
Design B	5	157	31.4	6.3
Design C	5	115	23.0	8.5

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Between Groups	496.5333	2	248.2667	43.56	3.23E-06	3.88529
Within Groups	68.4	12.0	5.7000
Total	564.9333	14

(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	43.56
p-value	0.0000

Reject H0: bottle design (Click to select)does have an impact on sales.

(b) Consider the pairwise differences μB – μA, μC – μA , and μC – μB. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Point estimate Confidence interval

μB –μA:14.00 , [9.97,18.03 ]

μC –μA: 5.60, [1.57, 9.63]

μC –μB: -8.40, [-12.43, -4.37]

Bottle design (Click to select) B maximizes sales.

(c) Find a 95 percent confidence interval for each of the treatment means μA, μB, and μC. Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Confidence interval

μA: [15.07, 19.73]

μB: [29.07,33.73 ]

μC: [20.67, 25.33]

MINITAB used. MINITAB output: