Question

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H₀: μ_D = 0 versus H_a: μ_D > 0 at significance level 0.01. (Use μ_D = μ_U − μ_A.)

Fabric
	1	2	3	4	5	6	7	8
U	36.3	55.0	51.2	38.5	43.2	48.8	25.6	49.5
A	28.5	20.0	46.0	34.0	36.0	52.5	26.5	46.5

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

State the conclusion in the problem context.

Reject H₀. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Reject H₀. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.    Fail to reject H₀. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to reject H₀. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

Answer 1

U	A	dbar
36.3	28.5	7.8
55	20	35
51.2	46	5.2
38.5	34	4.5
43.2	36	7.2
48.8	52.5	-3.7
25.6	26.5	-0.9
49.5	46.5	3

dbar = μ(before) - μ(after) = 7.2625
s(dbar)= 11.8714

SE = s(dbar)/sqrt(n)  
= 11.8714./sqrt(8)
= 4.1972

Test Statisitcs,
t = dbar/SE  
= 7.2625/4.1972

=1.73

p value = 0.1273

Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.