STATISTICS F/BUSINESS+ECONOMICS-TEXT
STATISTICS F/BUSINESS+ECONOMICS-TEXT
13th Edition
ISBN: 9781305881884
Author: Anderson
Publisher: CENGAGE L
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Chapter 13, Problem 34SE

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. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Brand
x y z
91 99 83
100 96 88
88 94 89
89 99 76
Expert Solution & Answer
Check Mark
To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34SE

Yes, there appear to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

State the hypotheses:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: Not all the population means are equal.

The level of significance is 0.05.

Software procedure:

Step by step procedure to obtain One-Way ANOVA using the MINITAB software:

  • Choose Stat > ANOVA > One-Way.
  • In Response, enter the column of values.
  • In Factor, enter the column of Brands.
  • Click OK.

Output using the MINITAB software is given below:

STATISTICS F/BUSINESS+ECONOMICS-TEXT, Chapter 13, Problem 34SE

From the Minitab output the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-valueα,, reject the null hypothesis H0

If p-value>α, fail to reject the null hypothesis H0

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

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Chapter 13 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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