Problem 11.1: A consumer preference study compares the effects of the 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 bottle sold in 24 hours at each supermarket is recorded, and displayed in the table below. Let $µ_A$, $µ_B$ and $µ_C$ represent mean daily sales using bottle designs A, B, and C, respectively. Figure 12.5 gives the Excel output of a one-way ANOVA of the bottle design study data.
Bottle Design
FIGURE 12.5 Excel Output of a One-Way ANOVA of the Bottle Design Study Data
A
B
C
SUMMARY
16
33
23
Groups
Count
Sum
Average
Variance
18
31
27
DESIGN A
5
83
16.6
5.3
19
37
21
DESIGN B
5
164
32.8
9.2
17
29
28
DESIGN C
5
124
24.8
8.2
13
34
25
ANOVA
Source of Variation
SS
df
MS
Between Groups
656.1333
2
328.0667
F
P-Value
F crit
43.35683
3.23E-06
3.88529
Within Groups
90.8
12
7.566667
Total
746.9333
14
Test the null hypothesis that $µ_A$, $µ_B$ and $µ_C$ are all equal by setting α = 0.05. That is, test for statistically significant differences between these group means at the 0.05 level of significance. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales?
Step 1: Ho:
Step 2: α =
VS
;
n df (df1) =
; d df (df2) =
Step 3: All ANOVA Tests are right-tailed F-Test.
Step 4: Test Statistic F:
Step 5: Critical Value
F Critical =
p-value =
Draw and label the rejection region.
Step 6.1:
Statistical Decision (Reject Ho vs Do not Reject Ho):
Step 6.2: Write up the conclusion and implication (use the complete sentence):