A toy manufacturer receives large shipments of electronic components that will be used in the dolls that it makes. It is too expensive to test every component to see whether it functions properly, so the manufacturer inspects a random sample of components from every shipment. The toy manufacturer does not accept any shipments unless there is evidence that fewer than 3% of the components are defective.
a. What are the null and alternative hypotheses for this situation?
b. Explain the Type I and Type II errors in the context of the component shipments.
c. From the toy manufacturer's point of view, which type of error would be the most important? Why?