Chapter 13, Problem 34E

Paper Towel Absorption. 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?

To determine

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

Answer to Problem 34E

Yes, there appears 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.

Assume that, ${\mu }_1$, ${\mu }_2$ and ${\mu }_3$ denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

$H_0:{\mu }_1={\mu }_2={\mu }_3$

Alternative hypothesis:

$H_a:$ At least one of the means is not equal.

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 the EXCEL:

• Enter the data in an EXCEL sheet.
• On Data tab in Analysis group, click Data Analysis.
• Select Anova: Single Factor.
• Click Ok.
• Click in the Input Range box, select the range $A$1: $C$5.
• Click in the Output range, select $G$1
• Click OK.

Output using the EXCEL software is given below:

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

Decision:

If $p\text{-value}\le \alpha ,$ reject the null hypothesis $H_0$.

If $p\text{-value}>\alpha ,$ fail to reject the null hypothesis $H_0$.

Conclusion:

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

That is, $p\text{-value}\left(=0.0134\right)<\alpha \left(=0.05\right)$.

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 $\alpha =0.05$ level of significance.