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 some fabric specimens.

Permafresh	Hylite
124	147
104	199
142	149
111	156
123

A consumer group suspects that there is a difference in recovery from wrinkles after washing. Specifically, they want to test the claim that there is a difference in recovery between using Permafresh and Hilite. To investigate this, they identified the mean recovery from wrinkles after washing by measuring the wrinkle recovery angle in degrees for a sample of fabrics using Permafresh, and a sample of fabrics using Hylite.

At the 5% level of significance, is there enough evidence to conclude that there is a difference in wrinkle recovery angle between Permafresh and Hylite?

It is often reasonable to conclude that measurements are normal in distribution. So it is reasonable to assume the population of wrinkle recovery angle is normal for both Permafresh and Hylite. Also assume that the data represents a SRS (simple random sample) of fabrics using Permafresh and Hylite.

1) Why is this a two sample independent means test? and Step 1: State the Claims which means to State the null and alternative hypotheses. Use correct math type. You may want to consider looking back at the symbols assignment from the beginning of class.

Answer 1

using excel>addin>phstat>two sample test

we ahve

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	5
Sample Mean	120.8
Sample Standard Deviation	14.51551
Population 2 Sample
Sample Size	4
Sample Mean	162.75
Sample Standard Deviation	24.47277
Intermediate Calculations
Population 1 Sample Degrees of Freedom	4
Population 2 Sample Degrees of Freedom	3
Total Degrees of Freedom	7
Pooled Variance	377.0786
Standard Error	13.0263
Difference in Sample Means	-41.9500
t Test Statistic	-3.2204
Two-Tail Test
Lower Critical Value	-2.3646
Upper Critical Value	2.3646
p-Value	0.0146
Reject the null hypothesis

Here claim is that there is a difference in wrinkle recovery angle between Permafresh and Hylite.
It is often reasonable to conclude that measurements are normal in distribution. So it is reasonable to assume the population of wrinkle recovery angle is normal for both Permafresh and Hylite. Also assume that the data represents a SRS (simple random sample) of fabrics using Permafresh and Hylite.

1) this is a two sample independent means test because two sample teken for this scenario is independent and taken with Simple random sampling and also the population from which these samples are drawn is given to normal. so it satisfy all the conditionfor independent sample t test

Step 1: the Claim is is that there is a difference in wrinkle recovery angle between Permafresh and Hylite

the null and alternative hypotheses are

Ho: u( Permafresh) = u(Hylite)

Ha: u( Permafresh) ≠ u(Hylite)

the value of test stat t = -3.2204

p value is 0.0146

since p value is less than 0.05 so we reject Ho and conclude that there is a difference in wrinkle recovery angle between Permafresh and Hylite