Answer Happy

EXAMPLE 8.5 | Alloy Adhesion An article in the Journal of Materials Engineering ["Instrumented Tensile Adhesion Tests on Plasma Sprayed Thermal Barrier Coatings" (1989, Vol. 11(4), pp. 275-282)] describes the results of tensile adhesion tests on 22 U-700 alloy specimens. The load at specimen failure is as follows (in megapascals): 19.8 15.4 11.4 19.5 10.1 18.5 14.1 8.8 14.9 7.9 17.6 13.6 0.01 O 0.025 O 0.05 0.95 O 0.975 7.5 12.7 X-a/2-1/√n≤ 13.71-2.080 (3.55)/√√22 ≤ 13.71-1.57 ≤ 16.7 11.9 15.4 11.9 15.8 11.4 The sample mean is = 13.71, and the sample standard deviation is s= 3.55. Figures 8.6 and 8.7 show a box plot and a normal probability plot of the tensile adhesion test data, respectively. These displays provide good support for the assumption that the population is normally distributed. We want to find a 95% CI on u. Since n = 22, we have n - 1 = 21 degrees of freedom for t, so fo.025,21 = 2.080. The resulting CI is ≤ x + 1a/2n-15/√n ≤ 13.71 +2.080 (3.55)/√22 ≤ 13.71 +1.57 12.14 < μ < 15.28 Referring to Example 8-5 above, the probability that the true mean, u, lies below 12.14 or above 15.28 is 15.4 11.4