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
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.
Ha: μx = μy = μzH0: μx = μy = μz
Ha: μxμyμz     H0: At least two of the population means are equal.
Ha: At least two of the population means are different. H0: μx = μy = μz
Ha: Not all the population means are equal. H0: μxμyμz
Ha: μx = μy = μz

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

p-value =

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.

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

The hypotheses are:

H0: μx = μy = μz
Ha: 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.

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