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, 11 were defective.

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

1. True
2. False
b. If the proportion of defectives in the sample is only slightly less than 12%, the difference could be due entirely to sampling variation, and it's not reasonable to conclude that the new process is better.
1. True
2. False

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.
1. True
2. False

Answer 1

a. If the proportion of defectives in the sample is only slightly less than 12%, the difference could be due entirely to sampling variation, and it's not reasonable to conclude that the new process is better

b. True

c. True

Explanation:

a. The percentage of defective circuits produced = 12%

Given that the percentage of defective circuits produced in the new process is 11% which is only slightly less than the observed 12%, the difference may be due to variation in the sample, as another sample of 100 in the new process cold produce more than 11 defective circuits

b. True. In every sample, there is a slight variation which can account for the difference

c. Given that the defectives in the sample is considerably less than 12%, then it would be more statistically evident that there is a difference in the two processes and the new process can be considered reasonably better

Therefore, the answer is; True