Electrical components are manufactured continuously on a production line. Extensive data show that when all machines are correctly adjusted, a fraction 0.026 of the components are defective. However,...

Electrical components are manufactured continuously on a production line. Extensive data show that when all machines are correctly adjusted, a fraction 0.026 of the components are defective. However, some settings tend to vary as production continues, so the fraction of defective components may increase. A sample of 420 components is taken at regular intervals, and the number of defective components in the sample is counted. If there are more than 16 defective components in the sample of420, the production line will be stopped and adjustments will be made.

(a) State the null hypothesis and alternative hypothesis in terms ofp.

(b) What is the observed level of significance if the number of defective components is just large enough to stop the production line?

(c) Suppose the probability that a component will be defective has increased to 0.040. Then what is the probability of a Type II error?