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. (a) One of the engineers suggests that the test proves that the new pro- cess is no better than the old process, since the proportion of defec- tives in the sample is the same. Is this conclusion justified? Explain. (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. (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?

Explanation / Answer

old method produced 12% of defective

A) IN THIS PART IT IS GIVEN THAT THE NEW METHOD ALSO PRODUCES 12 DEFECTIVE OUT OF 100 HENCE THE NUMBER WILL BE 12% WHICH IS NO BETTER THEN THE OLD METHOD. AS THE PROPORTION OF DEFECTIVE IS SAME IN BOTH THE TWO WE GET THE CLAIM IS JUSTIFIES..

B) HERE IT IS GIVEN THAT 11 ARE DEFECTIVE AMONG 100 WHICH IS EQUAL TO 11% WHICH IS 1% LESS THEN THE OLD METHOD. 1% BECOMES A LARGE NUMBER IF THE PRODUCTION IS MORE HENCE THE CLAIM THAT NEW METHOD IS BETTER IS JUSTIFIED.

C) FINDING 11 DEFECTIVE AMONG 12 PROVIDE BETTER EVIDENCE BECAUSE IT SHOWS 1% LESS THEN THE EARLIER 12%.

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