In: Statistics and Probability
"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 Hylite. 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.
2) Step 2: Collect the Data. This step means to
find the summary data for the sample, and to assess normality, and
to find the test statistic.
a) What are the sample means? Use 4 decimal places.
Permafresh: ______
Hylite: _______
b) What are the sample standard deviations? Use 4 decimal
places.
Permafresh: _____
Hylite: ________
c) Are the normality assumptions met? Is it reasonable to assume normality?
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.
2) This step means to find the summary data for the
sample, and to assess normality, and to find the test
statistic.
a) the sample means are
Permafresh:120.8000
Hylite:162.7500
b) the sample standard deviations are
Permafresh:14.5155
Hylite: 24.4728
c) Are the normality assumptions met? Is it reasonable to assume normality?
from the boxplot we can say that the data is normally distributed