Question 7.4: Methods for estimating strength and stiffness requirements s...
Methods for estimating strength and stiffness requirements should be conservative, in that they should overestimate rather than underestimate. The success rate of such a method can be measured by the probability of an overestimate. The article “Discrete Bracing Analysis for Light-Frame Wood-Truss Compression Webs” (M. Waltz, T. McLain, et al., Journal of Structural Engineering, 2000:1086-l093) presents the results of an experiment that evaluated a standard method (Plaut’s method) for estimating the brace force for a compression web brace. In a sample of 380 short test columns (4 to 6 ft in length), the method overestimated the force for 304 of them, and in a sample of 394 long test columns (8 to 10ft in length), the method overestimated the force for 360 of them. Find a 95% confidence interval for the difference between the success rates for long columns and short columns.
The number of successes in the sample of short columns is X = 304, and the number of successes in the sample of long columns is Y = 360. The numbers of trials are n_X = 380 and n_Y=394. We compute \tilde{n}_X=382, \tilde{n}_Y=396, \tilde{p}_X=(304+1) / 382=0.7984 and \tilde{p}_Y=(360+1) / 396=0.9116. The value of z_{\alpha/2} is 1.96.The 95% confidence interval is 0.9116-0.7984 \pm 1.96 \sqrt{(0.7984)(0.2016) / 382+(0.9116)(0.0884) / 396} , or 0.1132 ± 0.0490.