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 155 115 120 102 128

Hylite 184 168 198 167

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

The mean and the standard deviation for the Permafresh are: ¯ x = Round to 3 decimal places. s = Round to 3 decimal places?

The mean and the standard deviation for the Hylite are: ¯ x = Round to 3 decimal places. s = Round to 3 decimal places?

The standard error is: SE = Round to 3 decimal places?

The critical value from the distribution for a confidence interval of 99.9% is: 

t*= ?  Use degrees of freedom of 3. Use Technology Round to 3 decimal places.

Using the the answer from above (all rounded to 3 decimal places), calculate by hand a 99.9% confidence interval for the difference in mean wrinkle recovery angle: to . Hint Round to 3 decimal places.

Answer 1

Permafresh

\(\bar{x}=124 ; s=19.736\)

Hylite

\(\bar{x}=179.250 ; s=14.728\)

\(S E=\sqrt{\left(s_{1}^{2} / n_{1}\right)+\left(s_{2}^{2} / n_{2}\right)}\)

on putting values

\(\mathrm{SE}=11.495\)

\(=\)

\(t_{\text {critical }}=t_{0.001 / 2,3}=12.924\)

\(99.9 \% C I=(124-179.25) \pm 12.924 * 11.495\)

\(=-55.25 \pm 148.561\)

\(=(-203.811,93.311)\)