Question

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. We have summary information on air permeability (in cm3/cm2/sec) for two different types of plain weave fabric (see below). Cotton: 51.7,49.5,50.4,47.7,47.7,50 2,51.4,55 2,48.7,50.4,49.8,46.2 Acetate: 58.9,55.5,62.1,57.8,60.3,58.6,60.8,58.5,61.2 61.8,64.3,59.5 (1) Find a 90% confidence interval for the true difference in mean permeability, Acetate - Cotton ( ) Enter your answers correct to 2 decimal places. (2) What assumptions did you make to answer this question? Do they seem reasonable? Tick all that apply O Data are approximately normal. (Seems reasonable from the normal quantile plot.) O We have two independent random samples of measurements. (Whether this is satisfies depends on the study design.) Data are approximately normal. (But data are strongly skewed, from the normal quantile plot, so this is not reasonable.) The sample mean difference is approximately normal. (Seems reasonable since np(1-P) > 5.) Standard deviations are equal. (Seems reasonable, from the data.)

Answer 1

using minitab>stat>basic stat>two sample test

we have

Two-Sample T-Test and CI: Acetate, Cotton

Two-sample T for Acetate vs Cotton

N Mean StDev SE Mean
Acetate 12 59.94 2.32 0.67
Cotton 12 49.91 2.32 0.67

Difference = μ (Acetate) - μ (Cotton)
Estimate for difference: 10.033
90% CI for difference: (8.409, 11.658)
T-Test of difference = 0 (vs ≠): T-Value = 10.60 P-Value = 0.000 DF = 22
Both use Pooled StDev = 2.3177

ANs 1 ) 90% CI for difference: (8.41, 11.66)

Ans 2) option B , C and E is true