# ch09t.exe - 1 Exercises for Chapter 9 1. An article in the...

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Unformatted text preview: 1 Exercises for Chapter 9 1. An article in the journal of Engineering Fracture Mechanics, 1997, Vol. 56, No.1, 65-76 reports on a study regarding the effect of thickness in fatigue crack growth in aluminum alloy 2024-T351. Two groups of specimens were created, one with thickness of 3mm and the other with a thickness of 15mm. Each specimen had an initial crack length of 15mm. The same cyclic loading was applied to all specimens, and the number of cycles it took to reach a final crack length of 25mm was recorded. Suppose that for the group having thickness 3mm, a sample of size 36 gave X 1 = 160 , 592 and S 1 = 3 , 954, and for the group having thickness 15mm, a sample of size 42 gave X 2 = 159 , 778 and S 2 = 15 , 533. The scientific question is whether or not thickness affects fatigue crack growth. a) State the null and alternative hypotheses. b) State the test statistic and the rejection region, with level of significance . c) What assumptions, if any, are needed for the validity of the test procedure you specified in part b)? d) Carry out the test at level = 0 . 05, and state the p-value. e) Construct a 95% CI for the difference in the two means. Explain how the testing problem in a) can be conducted in terms of the CI, and check if the test result remains the same. 2. To compare the corrosion-resistance properties of two types of material used in underground pipe lines, specimens of both types are buried in soil for a 2-year period and the maximum penetration (in mils) for each specimen is measured. A sample of size 42 specimens of material type A yielded X 1 = 0 . 49 and S 1 = 0 . 19, and a sample of size 42 specimens of material type B gave X 2 = 0 . 36 and S 2 = 0 . 16. The scientific question is whether the two types of material have the same corrosion resistance. a) State the null and alternative hypotheses. b) State the test statistic and the rejection region, with level of significance . c) What assumptions, if any, are needed for the validity of the test procedure you specified in part b)? d) Carry out the test at level = 0 . 05, and state the p-value. e) Construct a 95% CI for the difference in the two means. Explain how the testing problem in a) can be conducted in terms of the CI, and check if the test result remains the same. 3. The lifetimes of a random sample of 49 batteries of brand A gave X 1 = 4 , 250 hours, and S 1 = 220 hours. The lifetimes of a random sample of 49 batteries of brand B gave X 2 = 4 , 040 hours, and S 2 = 190 hours. Find the p-value for testing H : 1- 2 = 100 versus H : 1- 2 &gt; 100, and use the p-value to determine if H is rejected at level = 0 . 05. 4. An article in the journal Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, 273-279) reported results of arthroscopic meniscal repair with an absorbable screw. For tears greater than 25 millimeters, 14 of 18 repairs were successful, while for tears less than 25 millimeters, 22 of 30 were successful....
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## This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.

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ch09t.exe - 1 Exercises for Chapter 9 1. An article in the...

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