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

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 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:

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

Alternative hypothesis:

$H_a:$ 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:

From the Minitab 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.