Question

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow.

Brand
x	y	z
90	99	83
100	97	87
87	93	90
95	99	72

At a 0.05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

State the null and alternative hypotheses.

H₀: μ_x = μ_y = μ_z
H_a: μ_x ≠ μ_y ≠ μ_zH₀: Not all the population means are equal.

H_a: μ_x = μ_y = μ_z    H₀: μ_x = μ_y = μ_z
H_a: Not all the population means are equal.

H₀: μ_x ≠ μ_y ≠ μ_z
H_a: μ_x = μ_y = μ_z

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

Do not reject H₀. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.   

Reject H₀. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

Do not reject H₀. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

Answer 1

Excel:

Data --> Data analysis --> Anova: Single Factor

Output:

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	416	2	208	6.077922	0.021363	4.256495
Within Groups	308	9	34.22222
Total	724	11

Answers:

H₀: μ_x = μ_y = μ_z
H_a: Not all the population means are equal.

test statistic = 6.08

p-value = 0.021

Reject H₀. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

(Reason : since p-value = 0.021 < 0.05, we reject H0)