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 alphaequals0.025​, 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 =0.51 0.64 0.49 1.53 0.37 0.41

Good stain removal = 0.58 2.72 0.60 0.98 0.64 1.31

Fair stain removal = 0.44 1.16 0.60

​(a) Identify the claim and state Upper H 0 and Upper H Subscript a. Choose the correct answer below.

A. Upper H 0​: mu 1 equals mu 2 equals mu 3 ​(claim) Upper H Subscript a​: At least one mean is different from the others.

B. Upper H 0​: mu 1 equals mu 2 equals mu 3 equals mu 4 equals mu 5 equals mu 6 Upper H Subscript a​: At least two means are different from the others.​ (claim)

C. Upper H 0​: At least one mean is different from the others.​ (claim) Upper H Subscript a​: mu 1 equals mu 2 equals mu 3 equals mu 4 equals mu 5 equals mu 6

D. Upper H 0​: mu 1 equals mu 2 equals mu 3 Upper H Subscript a​: 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. Subscript Upper N​, is = ​, and the degrees of freedom for the​ denominator, d.f. Subscript Upper D​, is = .

The critical value is Upper F 0equals = . ​(

Round to two decimal places as​ needed.)

The rejection region is F ▼= (less than or equals greater than greater than or equals less than). ​

(Round to two decimal places as​ needed.) ​(c) Calculate the test statistic.

Fequals =

​(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 not in the rejection​ region, reject Upper H 0.

B. Since F is not in the rejection​ region, fail to reject Upper H 0.

C. Since F is in the rejection​ region, reject Upper H 0.

D. Since F is in the rejection​ region, fail to reject Upper H 0.

Choose the correct interpretation below. There ▼= ( is, is not) enough evidence at the 2.5​% significance level to ▼= (dispute, support) the claim that the mean cost per ounce is ▼= (different for at least one product, the same for all three products) . Click to select your answer(s).

Answer 1