A certain process for manufacturing integrated circuits has been in use for a pe

Question

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. Justify your answers to the following questions 4) If the proportion of defectives in the sample is less than 12%, it is reasonable- to conclude that the new process is better. True or false? Justify 5) 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. True or false? Justify 6) 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. True or false? Justify

Explanation / Answer

4) The sample proportion is approximated value. And the true proportion may, be greater than 12%. Therefore, it is not reasonable to conclude that the new process is better.

5) True, because of sampling variation, the sample proportion slightly less than 12% gives no reason to conclude that the proportion of defective circuits produced by the new process is less than 12% and that the new process is better than the old one.

6)True, the random sample provides the proportion which is close to the true proportion. So, if the sample proportion is much less than 12%, it is very unlikely that the true proportion is greater than 12%. And it is reasonable to conclude that the new process is better than the old one.

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