Refer to the stress analysis on epoxy-repaired truss joints described in Exercise 7.20. Tests were conducted on epoxy-bonded truss joints made of wood to determine tolerances for actual glue line shear stress (Journal of Structural Engineering, Feb. 1986). The mean and standard deviation of the shear strengths (pounds per square inch) for a random sample of 100 Southern pine truss joints are

x̅ = 1,312           s = 422

a. Assuming the distribution of strength measurements is approximately normal, construct a 95% tolerance interval for 99% of the shear strengths.

b. Interpret the interval obtained in part b.

c. Explain how you could obtain a tolerance interval when the normality assumption is not satisfied.

Data from Exercise 7.20

Let (y̅₁ , s₁²) and (y̅₂ , s₂²) be the means and variances of two independent random samples of sizes n₁ and n₂, respectively, selected from normal populations with different means, μ₁ and μ₂, but with a common variance, σ².