Consider the accompanying data on breaking load (kg/25 mm width) for various fab
ID: 3430015 • Letter: C
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: ?D = 0 versus Ha: ?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.
Fabric 1 2 3 4 5 6 7 8 U 36.1 55.0 51.2 38.5 43.2 48.8 25.6 49.5 A 28.5 20.0 46.0 34.5 36.5 52.5 26.5 46.5Explanation / Answer
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.
43.4875 mean U 36.3750 mean A 7.1125 mean difference (U - A) 11.8893 std. dev. 4.2035 std. error 8 n 7 df