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.
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.
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.
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
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.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
Expert Solution
Step 1
Given the data on two different types of plain-weave fabric as
