Concept explainers
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?
Check whether there is a significant difference in the ability of the brands to absorb water at
Answer to Problem 34SE
Yes, there is a significant difference in the ability of the brands to absorb water.
Explanation of Solution
Calculation:
The data represent the absorbency rate for the three brands.
Assume that
The test hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
It is given that the level of significance as 0.05.
One-way ANOVA:
Software procedure:
Step-by-step procedure to obtain one-way ANOVA using EXCEL:
- Open the EXCEL.
- Enter x, y, and z in different columns.
- On Data tab in analysis group, click Data Analysis.
- Select Anova: Single Factor.
- Click OK.
- Click in the Input Range box, select x, y, and z.
- Click OK.
The output obtained using EXCEL software is shown below:
From the output, it is observed that the F-ratio is 7.23 and the p-value is 0.0134.
Decision:
If the
If the
Conclusion:
Here, the p-value is less than the level of significance.
That is,
Therefore, the null hypothesis is rejected.
Hence, there is sufficient evidence to infer that there is a significant difference in the ability of the brands to absorb water.
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