he void volume within a textile fabric affects comfort, flammability, and insulation properties. Permeability of a fabric refers to the accessibility of void space to the flow of a gas or liquid. An article gave summary information on air permeability (cm3/cm2/sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric: Fabric Type Sample Size Sample Mean Sample Standard Deviation Cotton 10 51.41 0.75 Triacetate 10 132.15 3.59Assuming that the porosity distributions for both types of fabric are normal, let's calculate a confidence interval for the difference between true average porosity for the cotton fabric and that for the acetate fabric, using a 95% confidence level. Before the appropriate t critical value can be selected, df must be determined: df = 0.5625 10 + 12.8881 10 2 (0.5625/10)2 9 + (12.8881/10)2 9 = 1.8092 0.1849 = (rounded to two decimal places) Thus we use ? = 9; the appendix table for critical values for t Distributions gives t0.025,9 = 2.262. The resulting interval is 51.41 − 132.15 ± (2.262) 0.5625 10 + 12.8881 10 = −80.74 ± (rounded to two decimal places) = (−83.36, ) (rounded to two decimal places)With a high degree of confidence, we can say that true average porosity for triacetate fabric specimens exceeds that for cotton specimens by between (rounded to two decimal places) and 83.36 cm3/cm2/sec.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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The void volume within a textile fabric affects comfort, flammability, and insulation properties. Permeability of a fabric refers to the accessibility of void space to the flow of a gas or liquid. An article gave summary information on air permeability (cm³/cm²/sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric:

Fabric Type	Sample Size	Sample Mean	Sample Standard Deviation
Cotton	10	51.41	0.75
Triacetate	10	132.15	3.59

Assuming that the porosity distributions for both types of fabric are normal, let's calculate a confidence interval for the difference between true average porosity for the cotton fabric and that for the acetate fabric, using a 95% confidence level. Before the appropriate t critical value can be selected, df must be determined:

df =

0.5625

12.8881

	2

(0.5625/10)²

(12.8881/10)²

1.8092

0.1849

(rounded to two decimal places)

Thus we use ? = 9; the appendix table for critical values for t Distributions gives t_0.025,9 = 2.262. The resulting interval is

51.41 − 132.15

(2.262)

0.5625

12.8881

−80.74 ± (rounded to two decimal places)

(−83.36, ) (rounded to two decimal places)

With a high degree of confidence, we can say that true average porosity for triacetate fabric specimens exceeds that for cotton specimens by between (rounded to two decimal places) and 83.36 cm³/cm²/sec.

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Step 1

Given the data on two different types of plain-weave fabric as

Fabric Type	Sample Size	Sample Mean	Sample Standard Deviation
Cotton	10	51.41	0.75
Triacetate	10	132.15	3.59

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