26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33
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26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. |
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(b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____
The critical value is F0=____
(Round to two decimal places as needed.)
The rejection region is F ▼
less than or equals≤
greater than>
less than<
greater than or equals≥
__
(Round to two decimal places as needed.)
(c) Calculate the test statistic.
F=__(Round to three decimal places as needed.)
(d) Decide to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. Choose the correct decision below.
A.
Since F is in the rejection region, fail to reject H0.
B.
Since F is not in the rejection region, fail to reject H0.
C.
Since F is in the rejection region, reject H0.
D.
Since F is not in the rejection region, reject H0.
Choose the correct interpretation below.
There
▼
is not
is
enough evidence at the
1%
significance level to
▼
support
dispute
the claim that the mean cost per ounce is
▼
different for at least one product
the same for all three products
.
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