The results of a study on the effectiveness of line drying on the smoothness of

Question

The results of a study on the effectiveness of line drying on the smoothness of fabric is summarized in the table below. Smoothness scores are provided for nine different types of fabric and five different methods: (1) machine dry, (2) Line dry, (3) line followed by 15 minute tumble, (4) line dry with softener and (5) line dry with air movement. Regarding the different types of fabrics as blocks, construct an ANOVA table. Using .05 level of significance, test to see if there is a difference in the true means scores for drying methods. Answer the following questions:

a. Construct the ANOVA table

b. State the null hypothesis, p value , calculated f value and decision (accept Ho or Reject Ho) for the Blocks(fabrics)

c. State the null hypothesis, p value , calculated f value and decision (accept Ho or Reject Ho) for the Treatment(drying method)

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

Explanation / Answer

a. Construct the ANOVA table

above

b. State the null hypothesis, p value , calculated f value and decision (accept Ho or Reject Ho) for the Blocks(fabrics)

null : there is no difference in the mean of different blocks

p-value = 3.86 *10^(-7)

F = 2.355

since p-value < 0.05

we reject the null , there is significant difference

c. State the null hypothesis, p value , calculated f value and decision (accept Ho or Reject Ho) for the Treatment(drying method)

null : there is no difference in the mean of five different methods

p-value = 8.77*10^(-8)

F = 3.0087

since p-value < 0.05

we reject the null , there is significant difference

1 2 3 4 5 2.2 1.5 2.7 1.5 1.9 3.6 1.3 2.8 1.7 1.8 3.3 2.5 2.8 2.5 1.9 2.6 1.4 2.4 1.3 1.6 3.6 2 3.6 2.4 2.3 3.5 2.1 2.8 2.1 2.2 3.8 1.3 2.8 2 1.6 4.2 3.4 3.8 3.1 3.1 3.4 2.4 2.9 1.6 1.7

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