True or false:a. If the proportion of defectives in the sample is less than 12%, it is reasonable to conclude that the new process is better.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.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.

In a population, the percentage or fraction which is not conforming to (defeating) is defined as a ratio of the population's figures of non-conforming goods to the sum of goods in the inhabitants, and the further discussion can be defined as follows:

In option A, it is wrong because the proportion of both the sample is simply an approximation. The real percentage could be more than 12%. Furthermore, the conclusion also that the new procedure is better cannot be reasonably concluded.
In options (b and c) both are correct because it is based on the explanation of whether, if the fraction of defective differences is bigger, we can only determine that its new procedure is better or not as a minor difference may occur from the variance of samples.

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