Question

In: Statistics and Probability

Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting...

Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α = 0.05, can you conclude that at least one mean cost per ounce is different from the others?

Very Good	.47	.49	.41	.37	.48	.51
Good	.60	.64	.58	.75	.46
Fair	.34	.46	.44	.60

Expert Solution

Null Hypothesis, Ho:

There is no significant difference in the means cost per ounce for toothpaste exhibiting very good stain removal, good stain removal, and fair stain removal i.e.

Alternative Hypothesis, Ha:

There exists at least toothpaste for which the mean cost per 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:

Treatment Groups	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 of significance.

Conclusion:

There exists at least toothpaste for which the mean cost per ounce is significantly different i.e. for at least one

orchestra answered 2 years ago

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