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
91	100	84
99	95	88
89	93	90
85	104	74

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

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 not 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 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

For the given data set anova testing can be done in excel tool.

The hypotheses are:

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

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
X	4	364	91	34.66667
Y	4	392	98	24.66667
Z	4	336	84	50.66667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	392	2	196	5.345455	0.029505	4.256495
Within Groups	330	9	36.66667
Total	722	11

The test statistic:

F=5.35

P-value:

P-value calculated for F statistic as:

P-value=0.0295

Conclusion:

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

Since P-value< 0.05.