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
148	162
119	149
141	143
153	166
157

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= Round to 3 decimal places.
   
   s= Round to 3 decimal places.
   
2. The mean and the standard deviation for the Hylite are:
   
   ¯x= Round to 3 decimal places.
   
   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 99% 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 99% confidence interval for the difference in mean wrinkle recovery angle:
   
   ____________ to _________ Hint Round to 3 decimal places.

Answer 1

from excel functions:

a) mean for the Permafresh x- =average(Array) =143.600

standard deviation for Permafresh s=stdev(array) =14.993

mean for the Hylite =155.00

standard deviation for the Hylite =10.801

std error SE =√(S21/n1+S22/n2)=sqrt(14.993^2/5+10.801^2/4)=

8.609

for 99 % CI & 3 df value of t=

5.841

from excel: t.inv(0.995,3)

Point estimate of differnce =x1-x2     =		-11.400
for 99 % CI & 3 df value of t=		5.841
margin of error E=t*std error                   =		50.285
lower bound=mean difference-E     =		-61.685
Upper bound=mean differnce +E      =		38.885
from above 99% confidence interval for population mean =(-61.685,38.885)