Chapter 4, Problem 34E

An in-line tester is used to evaluate the electrical function of printed circuit boards. This machine counts the number of defects observed on each board. A random sample of 1,000 boards contains a total of 688 defects. Is it reasonable to conclude that the mean occurrence rate of defects is λ = 1? Use the results of part (a) of Exercise 4.26 and assume that α = 0.05.

4.26. The cooling system in a nuclear submarine consists of an assembly pipe through which a coolant is circulated. Specifications require that weld strength must meet or exceed 150 psi.

1. (a) Suppose the designers decide to test the hypothesis H₀: μ = 150 versus H₁: μ > 150. Explain why this choice of alternative is preferable to H₁: μ < 150.
2. (b) A random sample of 20 welds results in $\bar{x}=153.7$ psi and s = 11.5 psi. What conclusions can you draw about the hypothesis in part (a)? Use α = 0.05.