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
92	98	84
101	95	87
88	93	88
87	102	77

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

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

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
x	4	368	92	40.66667
y	4	388	97	15.33333
z	4	336	84	24.66667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	344	2	172	6.396694	0.018691	4.256495
Within Groups	242	9	26.88889
Total	586	11

Null and alternative hypotheses :

H₀: μ_x = μ_y = μ_z

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

test statistic :

From the above output

test statistic = 6.40

p-value = 0.0187

conclusion :

P value < L.o.s

0.0187 < 0.05

So reject H0

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