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.

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?

2) 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.

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? Since the data size is small in both samples, indicate this by looking at the statement of the problem. Is it reasonable to assume normality?

3) Step 3: Assessment of Evidence. Find the pvalue and upload an image of the normal curve with the test statistic indicated and the correct area of the curve shaded. This shaded area is the pvalue.

a) What is the pvalue? Use 4 decimal places. b) Upload an image of the normal curve with the test statistic indicated and the correct area of the curve shaded. This shaded area is the pvalue.

4) Step 4: Conclusion. State your conclusion. Either reject or fail to reject H0H0 , indicate why, then write the conclusion in terms of the problem.

Permafresh	Hylite
124	147
104	199
142	149
111	156
123

Answer 1

	Permafresh	Hylite
	124	147
	104	199
	142	149
	111	156
	123
Mean	120.8	162.75
SD	14.5155089	24.47277
n	5	4

α=0.05

1)

Because samples from independent events

2)

Hypothesis:

H0 : μ1​ = μ2

Ha : μ1​ not = μ2​​

a and b)

Mean	X1 bar = 120.8	X2 bar = 162.75
SD	S1 = 14.5155089	S2 = 24.47277
n	n1 = 5	n2 = 4

3)

Assumptions are met, samples are independent and normally distributed

Equal variance test

F stat = S1^2/S2^2 = 0.352

F critical :

FL​=0.1 and FU​=15.101

FL < Fstat < FU, Do not reject H0

Use F table for critical values

T test:

df = 7

∣t∣ > t critical = 2.365, To reject H0

Use t table for critical value

Sp^2

377.0789686

((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)

t

-3.220398035

(X1 bar-X2 bar )/SQRT(Sp*(1/n1 + 1/n2))

P value

0.014645322

T.DIST.2T(-ts,df)

4)

Conclusion:

P value < 0.05, reject H0

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