Question

"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the previous exercise:

Permafresh	Hylite
140	167
109	195
106	175
128	157
139

A manufacturer wants to know how large is the difference in mean wrinkle recovery angle.

1. The mean and the standard deviation for the Permafresh are:
   
   ¯x=x¯= Round to 3 decimal places.
   
   s=s= Round to 3 decimal places.
   
2. The mean and the standard deviation for the Hylite are:
   
   ¯x=x¯= Round to 3 decimal places.
   
   s=s= Round to 3 decimal places.
   
3. The standard error is:
   
   SE = Round to 3 decimal places.
   
   The critical value from the distribution for a confidence interval of 95% is:
   
   t*= Use degrees of freedom of 3. Use Technology Round to 3 decimal places.
   
4. Using the the answer from above (all rounded to 3 decimal places), calculate by hand a 95% confidence interval for the difference in mean wrinkle recovery angle:
   
   to . Hint Round to 3 decimal places.

Answer 1

a)

Sample #1   ---->   Permafresh
mean of sample 1,    x̅1=   124.400
standard deviation of sample 1,   s1 =    16.165
size of sample 1,    n1=   5
      
b)

Sample #2   ---->    Hylite
mean of sample 2,    x̅2=   173.500
standard deviation of sample 2,   s2 =    16.114
size of sample 2,    n2=   4

c)

std error , SE =    √(s1²/n1+s2²/n2) =    10.825

t-critical value , t* =    3.182 (excel formula =t.inv(α/2,df)

d)

margin of error, E = t*SE =    3.1824   *   10.825   =   34.45
                  
difference of means = x̅1-x̅2 =    124.4000   -   173.500   =   -49.100
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    -49.1000   -   34.4494   =   -83.549
Interval Upper Limit = (x̅1-x̅2) + E =    -49.1000   -   34.4494   =   -14.651

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