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			29			23
	18			30			24
	17			33			22
	14			33			23
	17			31			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	83	16.6	2.3
Design B	5	156	31.2	3.2
Design C	5	113	22.6	1.3

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Between Groups	538.5333	2	269.2667	118.79	3.23E-06	3.88529
Within Groups	27.2	12.0	2.2667
Total	565.7333	14

(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: [, ]

(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: [, ]

(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

Groups	Count	Sum	Average	Variance
Design A	5	83	16.6	2.3
Design B	5	156	31.2	3.2
Design C	5	113	22.6	1.3

c) confidence interval = mean t* SE

t = 2.776 at 95 % confidence interval for two tail test(4 degree of freedom)

SE = Standard error = Square root of (variance /sample size)

sample size = 5

for design A

16.6 2.776 *Square root of (2.3/5)

16.6 2.776*.6782

16.6 1.88

so, 14.72 to 18.48

for design B

31.20 2.776* Square root of(3.2/5)

31.20 2.22

28.98 to 33.42

for design C

22.6 2.776 * square root of(1.3/5)

22.6 1.42

21.18 to 24.02

so confidence interval

A = 14.72 to 18.48

B = 28.98 to 33.42

C= 21.18 to 24.02