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

alpha

equals0.05

,
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

0.64

0.33

0.44

0.35

2.73

1.33

0.51

0.42

0.34

1.53

0.75

nothing

0.48

0.58

nothing

0.47

1.38

nothing

(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

Upper H Subscript a

:
At least one mean is 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

D.

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)

(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

nothing

,

and the degrees of freedom for the denominator,

d.f. Subscript Upper D

,

is

nothing

.

The critical value is
Upper F 0

equalsnothing

.

(Round to two decimal places as needed.)

The rejection region is
F

▼

greater than or equals

greater than

less than

less than or equals

nothing

.

(Round to two decimal places as needed.)

(c) Calculate the test statistic.

Fequals

nothing

(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, fail to reject
Upper H 0

.

B.

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

.

C.

Since F is not 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 not

is

enough evidence at the
5

%
significance level to

▼

support

dispute

the claim that the mean cost per ounce is

▼

the same for all three products

different for at least one product

.

Click to select your answer(s).

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

alpha

equals0.05

,

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
0.64

0.33

0.44

0.35

2.73

1.33

0.51

0.42

0.34

1.53

0.75

nothing

0.48

0.58

nothing

0.47

1.38

nothing

(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

Upper H Subscript a

:

At least one mean is 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

D.

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)

(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

nothing

,

and the degrees of freedom for the denominator,

d.f. Subscript Upper D

,

is

nothing

.

The critical value is

Upper F 0

equalsnothing

.

(Round to two decimal places as needed.)

The rejection region is

F

▼

greater than or equals

greater than

less than

less than or equals

nothing

.

(Round to two decimal places as needed.)

(c) Calculate the test statistic.

Fequals

nothing

(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, fail to reject

Upper H 0

.

B.

Since F is in the rejection region, reject

Upper H 0

.

C.

Since F is not 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 not

is

enough evidence at the

5

%

significance level to

▼

support

dispute

the claim that the mean cost per ounce is

▼

the same for all three products

different for at least one product

.

Click to select your answer(s).

Accepted Answer

(a)
Let μ1,μ2,μ3 be the population mean costs per ounce of toothpastes exhibiting very good stain​…