Chapter 10.2, Problem 22E

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is lower for the robots than for human assemblers. Let p denote the proportion of defective installations for the robots. It is known that human assemblers have a defect proportion of 0.02.

1. a. Which of the following pairs of hypotheses should the manufacturer test:

$H_0:p=0.02\text{versus}{H}_a:p< 0.02$

or

$H_0:p=0.02versus{H}_a:p> 0.02$

Explain your answer.

1. b. In the context of this exercise, describe Type I and Type II errors.
2. c. Would you prefer a test with α = 0.01 or α = 0.10? Explain your reasoning.