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 Datal B 29 33 32 A 19 18 16 17 18 33 32 CAMERAS ANOVA Source of с 24 F= p-value= 23 26 23 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. SUMMARY GroupsCount Sum AverageVariance 5 88 17.6 24 Design 1.3 A Design 5 159 31.8 2.7 B Design 5 120 24.0 1.5 C Variation Between Groups Within Groups Total SS 505.7333 22.0 12.0 527.7333 14 df 2 252.8667 137.93 1.8330 HO: bottle design MS (a) Test the null hypothesis that μA, HB, and μc are equal by setting a = .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.) Point estimate Confidence interval μB -μA: μC-μA: |ỤC –UB: F P-Value F crit 5.25E- 09 have an impact on sales. does does not 3.88529 (b) Consider the pairwise differences HB - HA, HC - HA, and μC - HB. 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.)
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 Datal B 29 33 32 A 19 18 16 17 18 33 32 CAMERAS ANOVA Source of с 24 F= p-value= 23 26 23 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. SUMMARY GroupsCount Sum AverageVariance 5 88 17.6 24 Design 1.3 A Design 5 159 31.8 2.7 B Design 5 120 24.0 1.5 C Variation Between Groups Within Groups Total SS 505.7333 22.0 12.0 527.7333 14 df 2 252.8667 137.93 1.8330 HO: bottle design MS (a) Test the null hypothesis that μA, HB, and μc are equal by setting a = .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.) Point estimate Confidence interval μB -μA: μC-μA: |ỤC –UB: F P-Value F crit 5.25E- 09 have an impact on sales. does does not 3.88529 (b) Consider the pairwise differences HB - HA, HC - HA, and μC - HB. 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:s
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
A1918 16 17 18
А
B
29
33
32
33
32
The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.
Design
C
SUMMARY
GroupsCount Sum AverageVariance
Design 5 88 17.6
A
Design 5 159 31.8
B
5 120 24.0
с
24
23
26
23
24
ANOVA
Source of
Variation
Between
Groups
Within Groups
Total
|F=
p-value =
SS
df
505.7333 2 252.8667 137.93
1.8330
22.0 12.0
527.7333 14
HO: bottle design
1.3
2.7
1.5
(a) Test the null hypothesis that μA, MB, and μc are equal by setting a = .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.)
Point estimate Confidence interval
μB -μA:
μC -μA:
|uC —UB:
1, [
₂ [
1,[
MS
F P-Value F crit
5.25E-
09
-
have an impact on
sales.
does
does not
(b) Consider the pairwise differences μB HA, HC HA, and μC MB. 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.)
3.88529
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