Question

The void volume within a este fabric afects comfort, formability, and insulation properties. Porability of a fabric refers to the city of void space to the flow of a gas orquid. We have summary Information on air permeability in cm ? c) for two different types of plain weave fabric below) Cotton: 51.0.43.6,50.447.747.7.502,51 4.552.48.7.50.449.8.46.1 Ace: 58 0.55.5.62.1,578.00.3.5.6.60 3.585.61.2.61.8.643.50.5 (1) Find a 95% confidence interval for the true diference in mean permeability "Acreme - "Comon 1 Number Number Enter your answers come to 2 decimal places 1) What assumptions did you make to answer the question? Do they seem reasonable? Tick all that apply Duts are prey normal (But data are strongly skewed, from the normal quartile plot, so this is not reasonable) Standard deviations we equal (Seomra rom data) We have two independent random samples of measurements. What this is satisfies depends on the study design) Dana are approximately normal Soms reasonable from the normal quartie plot.) The sample manierence is approximately normal (Seems reasonable since

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Answer 1

Solution: We need to construct the 95% confidence interval for the difference between the population means Hi - M9, for the case that the population standard deviations are not known. The following information has been provided about each of the samples: Sample Mean 1 (X) = 49.93 Sample Standard Deviation 1 (81) 2.35 12 Sample Size 1 (Ni) = Sample Mean 2 (2) = Sample Standard Deviation 2 (S2) 59.94 2.32 Sample Size 2 (N2) = 12 Based on the informationa provided, we assume that the population variances are unequal, so then the number of degrees of freedom is computed as follows: df = (sỉ/n + s/nay? 2 = 23.996 + /n22 72 +1 7+1 The critical value for a = 0.05 and df = 23.996 degrees of freedom iste = t1-a/2:1-1 = 2.064. The corresponding confidence interval is computed as shown below: Since we assume that the population variances are unequal, the standard error is computed as follows: si så se + ni n2 = 2.352 12 + 2.322 12 0.953 Now, we finally compute the confidence interval: CI (X1 - X, - te X se, X1 - X, +te X se) (49.93-59.94 2.064 x 0.953, 49.93 - 59.94 + 2.064 x 0.953) = (-11.977,-8.043) Therefore, based on the data provided, the 95% confidence interval for the difference between the population means Li - uz is -11.977<Mi - HO < 8.043, which indicates that we are 95% confident that the true difference between population means is contained by the interval (-11.977,-8.043).