Question

# In a completely randomized experimental design, three brands of paper towels were tested for their ability...

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: μx = μy = μz
Ha: μxμyμzH0: Not all the population means are equal.

Ha: μx = μy = μz    H0: μx = μy = μz
Ha: Not all the population means are equal.

H0: μxμyμz
Ha: μx = μy = μz

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

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

=

p-value =

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.

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

H0: μx = μy = μz
Ha: 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)

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