Question

The 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 6ft 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 the lower limit of the 95% confidence interval for the difference between the success rates for long columns and short columns. (4 decimal places)

Answer 1

here we will use z test for two proportions

using minitab >stat>basic stat>2 proportions

we have

Test and CI for Two Proportions

Sample X N Sample p
short test 1 304 380 0.800000
long test 2 360 394 0.913706

Difference = p (1) - p (2)
Estimate for difference: -0.113706
95% CI for difference: (-0.162554, -0.0648567)
Test for difference = 0 (vs ≠ 0): Z = -4.56 P-Value = 0.000

the lower limit of the 95% confidence interval for the difference between the success rates for long columns and short columns is -0.1626