The table to the right shows the cost per ounce (in dollars) for a random sample

Question

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 = 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 vanances. Very good | Good | Fair stain | stain stain n removal removal removal 0.49 0.35 0.48 1.57 0.51 0.64 0.34 1.14 0.46 0.58 2.74 0.98 0.75 0.60 1.38 (a) Identify the claim and state Ho and Ha. Choose the correct answer below. Ha: At least two means are different from the others. (claim) Ha: At least one mean is different from the others. 0 D. Ho: At least one mean is different from the others. (claim) Ha: At least one mean is different from the others. (claim) (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 2, and the degrees of freedom for the denominator, d.f.p, is 12

Explanation / Answer

The statistical software output for this problem is:

ANOVA table

Hence,

b) Critical value is F0 = 6.93

c) Test statistic = 1.166

Source DF SS MS F-Stat P-value Columns 2 0.92761 0.463805 1.165807 0.3446 Error 12 4.7740833 0.39784028 Total 14 5.7016933

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