Question by : stats problem!! How large is the difference in mean wrinkle recovery angle?
the reason for durable press treatment is to reduce wrinkling. “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 136 135 132 137 134
Hylite 143 141 146 141 145
How large is the difference in mean wrinkle recovery angle? Give a 95% confidence interval.
A. 6 to 10.8
B. 5.6 to 11.2
C. 5.3 to 11.5
D. 4.7 to 12.1
Best answer:
Answer by cidyah
Sample 1 size 5
Sample 2 size 5
Sample 1 mean 134.8
Sample 2 mean 143.2
Sample 1 S.D. 1.7205
Sample 2 S.D. 2.0396
Pooled S.D = [(n1-1)s1^2+(n2-1)s2^2]/(n1+n2-2)
Pooled variance s = [(4)(2.96012)+(4)(4.159968))] / (8) =
Pooled variance s^2 = 3.560044
Standard error of difference in means = sqrt(1/n1+1/n2) times sqrt(s^2)
Standard error of difference in means = (0.632456)(1.886808)
= 1.193322 (denominator of t)
t = (mean1-mean2) / SE = (134.8 – 143.2) /1.193322
t = -7.039172
Degrees of freedom = 8
t-critical value = 2.306
95 % Confidence interval is 8.4 ± (2.306)(1.193322)
= 5.6 to 11.2
Note:
A two-sample independent t-test has been performed assuming equal population variances.
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