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 a random sample of fabric specimens. Assume the populations are approximately normally distributed with unequal variances. A manufacturer believes that the mean wrinkle recovery angle for Hylite is better. A random sample of 25 Permafresh (group 1) and 20 Hylite (group 2) were measured. Test the claim using a 10% level of significance.

ermafresh	Hylite
127	148
132	148
157	144
122	149
140	148
144	129
134	142
129	139
116	148
165	138
115	136
146	141
152	144
111	134
120	146
135	149
119	134
142	139
119	133
134	140
100
141
123
167
127

Select the correct symbols.

H₀: =__________ _____________ ___________
H₁: =__________ _____________ ___________

Test Statistic= (Give answer to 4 decimal places)

p-value=___________ (Give answer to 4 decimal places)

Based on the above we choose to:

Fail to reject the null hypothesis

Accept the alternative hypothesis

Reject the null hypothesis

Accept the null hypothesis

The correct summary would be:

There is enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

There is not enough evidence to reject the claim

that the mean wrinkle recovery angle for Hylite is better.

Answer 1

The statistical software output for this problem is:

Two sample T hypothesis test:
μ₁ : Mean of ermafresh
μ₂ : Mean of Hylite
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ < 0
(without pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
μ1 - μ2	-8.77	3.6025802	31.65498	-2.4343663	0.0104

Hence,

Hypotheses:

Ho: μ₁ = μ₂
H₁ : μ₁ < μ₂

Test statistic = -2.4344

P - value = 0.0104

Reject the null hypothesis

There is enough evidence to support the claim