The void volume within a textile fabric effects comfort, flammability, and insul
ID: 3248893 • Letter: T
Question
The void volume within a textile fabric effects 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 (cm^3/cm^2sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric: Assuming that the porosity distributions for both types of fabric are normal, lets 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 = (0.6241/10 + 12.7449/10)^2/(0.6241/10)^2/9 + (12.7449/10)^2 = 1.7873/0.1809 = (rounded to two decimal places) Thus we use v = 9; the appendix table for critical values for t Distributions gives t_0.025, 9 = 2.262. The resulting interval is 51.31 - 135.17 plusminus (2.262) Squareroot 0.6241/10 + 12.7449/10 = -83.86 plusminus (round to two decimal places) = (-86.48, round to two decimal place With d 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 86.48 cm^3/cm^2/sec.Explanation / Answer
Given
95% Confidence interval for difference of means
where df= 10
t critical value at 5% level with 10 df=2.23
Hence 95% CI for difference of means is
(-86.44,-81.28)
x bar 51.31 y bar 135.17 n1 10 n2 10 s1 0.79 s2 3.57Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.