Question

HW # 10-Chapter 19 (20pts for turned in on time) (21pts)"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. There are two commercial processes for durable press: Permafresh and Hylite. A study wants to show if those 4. two processes will reduces the strength of the fabric in the same extent. Here are some data in terms of pull (in pounds) needed to tear the fabric as below. 30.7 23.9 30.0 27.0 29.5 22.1 27.6 24.2 32.3 21.8 Permafresh 29.9 Hylite 28.7 28.8 25.4 (1) (17pts)Assume the population variance between two processes are the same, perform an appropriate test on the data.(Refer to the mean and standard deviation calculation for both groups to HW8 question #3) (2) (4pts)What type of error could you make based on your inference? Please explain the type of error in context words

Answer 1

Following is the output of descriptive statistics generated by excel:

Descriptive statistics
	Permafresh, X1	Hylite, X2
count	7	7
mean	29.814	24.743
sample standard deviation	1.486	2.538
sample variance	2.208	6.440
minimum	27.6	21.8
maximum	32.3	28.8
range	4.7	7

(a)

Here we have 77 =29.814, 5-1.486, = 7 x3 =24.743, s, -2.538, n = 7 Hypotheses are: H:44-, = 0 H :14 -\, 0 Test is two tailed. Level of significance: a=0.05 Since we can assume that variances are equal so degree of freedom of t test will be: df = n +-2 =12 The pooled standard deviation is: (n-1) s 1 + (n - 175-2 -2,0796 PV 1 +n -2 Test Statistics: (5-7)-(4-us) -= ((29.814-24.743)-0)/(2.0796* sqrt((1/7)+(1/7))) 11 1 - +- ym. m = 4.56 Critical value: 2.179 Rejection Region: If|t| >2.179, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis. P-value: P-value=0.0007 Decision: Since p-value is less than level of significance so we reject the null hypothesis. Excel function for critical value: Excel function for p-value: TINV(0.05,12) =TDIST(4.56,12,2)

Conclusion: There is evidence to conclude that two fabrics do not reduce the strength of fabric at same extent

(b)

Since we reject the null hypothesis so type I error is possible. That is, we may incorrectly conclude that two fabrics do not reduce the strength of fabric at same extent while actually they did.