Chapter 1.1, Problem 6E

Refer to Exercise 5. True or false:

1. a. If the proportion of defectives in the sample is less than 12%, it is reasonable to conclude that the new process is better.
2. b. If the proportion of defectives in the sample is only slightly less than 12%, the difference could well be due entirely to sampling variation, and it is not reasonable to conclude that the new process is better.
3. c. If the proportion of defectives in the sample is a lot less than 12%, it is very unlikely that the difference is due entirely to sampling variation, so it is reasonable to conclude that the new process is better.

5.    A certain process for manufacturing integrated circuits has been in use for a period of time, and it is known that 12% of the circuits it produces are defective. A new process that is supposed to reduce the proportion of defectives is being tested. In a simple random sample of 100 circuits produced by the new process, 12 were defective.

1. a. One of the engineers suggests that the test proves that the new process is no better than the old process, since the proportion of defectives in the sample is the same. Is this conclusion justified? Explain.
2. b. Assume that there had been only 11 defective circuits in the sample of 100. Would this have proven that the new process is better? Explain.
3. c. Which outcome represents stronger evidence that the new process is better: finding 11 defective circuits in the sample, or finding 2 defective circuits in the sample?