Consider the accompanying data on breaking load kg25 mm widt

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: ?_D = 0 versus H_a: ?_D > 0 at significance level 0.01. (Use

?_D = ?_U ? ?_A.)

State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)

Compute the test statistic value. (Round your answer to three decimal places.)
t =

State the conclusion in the problem context.

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

Reject H₀. The data suggests a significant mean difference in breaking load for the two fabric load conditions.

Solution

the critical region is one-sided

The degree of freedom =n-1=8-1=7

Given a=0.01, the critical value is t(0.01, df=7) =2.998 (from student t table)

the rejection region is if t>2.998, we reject Ho.

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the test statistic value:

t=mean difference/ (s/vn)

=1.692

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