Chapter 11, Problem 50SE

The results of a study on the effectiveness of line drying on the smoothness of fabric were summarized in the article “Line-Dried vs. Machine-Dried Fabrics: Comparison of Appearance, Hand, and Consumer Acceptance” (Home Econ. Research J., 1984: 27–35). Smoothness scores were given for nine different types of fabric and five different drying methods: (1) machine dry, (2) line dry, (3) line dry followed by 15-min tumble, (4) line dry with softener, and (5) line dry with air movement. Regarding the different types of fabric as blocks, construct an ANOVA table. Using a .05 significance level, test to see whether there is a difference in the true mean smoothness score for the drying methods.

Drying Method
Fabric		1	2	3	4	5
	Crepe	3.3	2.5	2.8	2.5	1.9
	Double knit	3.6	2.0	3.6	2.4	2.3
	Twill	4.2	3.4	3.8	3.1	3.1
	Twill mix	3.4	2.4	2.9	1.6	1.7
	Terry	3.8	1.3	2.8	2.0	1.6
	Broadcloth	2.2	1.5	2.7	1.5	1.9
	Sheeting	3.5	2.1	2.8	2.1	2.2
	Corduroy	3.6	1.3	2.8	1.7	1.8
	Denim	2.6	1.4	2.4	1.3	1.6

To determine

Test the hypothesis to see whether there is any significant difference in the mean smoothness score due to the drying methods at 5% level of significance.

Answer to Problem 50SE

There is sufficient of evidence to conclude that there is significant difference in the mean smoothness score due to the drying methods at 5% level of significance.

Explanation of Solution

The data shows the mean smoothness of the fabric for five levels of drying methods with nine different types of fabrics..

Calculation:

$H_{0A}:{\alpha }_1={\alpha }_2={\alpha }_3={\alpha }_4={\alpha }_5=0$

There is no significant difference in the mean smoothness with respect to the five levels of drying methods.

$H_{aA}:\text{At least one of the }\alpha \text{'}s\ne 0$

There is difference in the mean smoothness with respect to the five levels of drying methods.

Software procedure:

Step by step procedure to find the test statistic using Minitab is given below:

• Click on Stat>ANOVA>Two-Way Analysis of Variance.
• Under Response, enter the column of mean smoothness.
• Under Row factor, enter the column of drying method.
• Under column factor, enter the column of fabric.
• Click OK.

Output obtained from MINITAB is given below:

Conclusion:

For drying methods:

The P-value for the drying methods is 0.000 and the level of significance is 0.05.

Here, the P-value is lesser than the level of significance.

That is, $0.000\left(=P\text{-value}\right)<0.05\left(=\alpha \right)$

Thus, the null hypothesis is rejected

Hence, there is sufficient evidence to conclude that there is an effect of drying methods on the mean smoothness of the fabric at 5% level of significance.