Toothpaste The table shows the
Toothpaste The table shows the costs per ounce (in dollars) fora sample of toothpastes exhibiting very good stain removal, goodstain removal, and fair stain removal. At α = 0.05, can youconclude that at least one mean cost per ounce is different fromthe others?
|
Very Good |
.47 |
.49 |
.41 |
.37 |
.48 |
.51 |
|
Good |
.60 |
.64 |
.58 |
.75 |
.46 |
|
|
Fair |
.34 |
.46 |
.44 |
.60 |
Answer:
Null Hypothesis, Ho:
There is no significant difference in the means cost perounce for toothpaste exhibiting very good stain removal, good stainremoval, and fair stain removal i.e.
Alternative Hypothesis, Ha:
There exists at least toothpaste for which the mean costper ounce is significantly different i.e. 
for at least one 
Test Statistics: Under Ho,
where k = number of groups = 3 and,
n = number of observations = 15
Calculations:
| TreatmentGroups | ni |  |
si |
| Very Good | 6 | 0.455 | 0.0536 |
| Good | 5 | 0.606 | 0.1048 |
| Fair | 4 | 0.46 | 0.1071 |
So,
and , 
Decision:
Since, p-value = 0.02951 < 
, so we reject the Null Hypothesis at 5% level ofsignificance.
Conclusion:
There exists at least toothpaste for which the mean costper ounce is significantly different i.e. for at least one
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