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 process is no better than the old process, since the proportion of defectives 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?

Answer

Step 1 of 3</p>

a) No,

Because of sampling variation

We don’t know exactly the proportion of defective circuits produced by the new system

We can only say that the proportion of defective circuits is close to 12%

We can’t say the weather proportion of defective circuits are more than 12%,

or equal to 12%, or less than 12%.

Hence we can’t conclude that new process is not better.

Step 2 of 3</p>

b) No, Because of sampling fluctuation,

The no. of defectives defective circuits 11 is very close to 12

Hence It is not proven that the new process is better.