A manufacturer of computer memory chips produces chips in lots of
1000. If nothing has gone wrong in the manufacturing process, about
5 chips in each lot would be defective, but if something does go wrong,
there could be far more defective chips. If something goes wrong with
a given lot, they discard the entire lot. It would be prohibitively expensive
to test every chip in every lot, so they want to make the decision of
whether or not to discard a given lot using a hypothesis test on the
number of defective chips in a random sample with replacement. The
company decides that they can afford to test 10 chips from each lot.
There is a tradeoff between the cost of eroneously discarding a good
lot, and the cost of warranty claims if a bad lot is sold. The next few
problems refer to this scenario."
I know that the type 1 error is a good lot gets discarded and a type 2
error is a bad lot isn't discarded. I also figured out that sample size
has a hypergeometric distribution because N=1,000, G<=5, and n=100.
1. To have a chance of at most 1% of discarding a lot given that the lot
is good, the test should reject if the number of defectives in the sample
of size 100 is greater than or equal to:.
2. In that case, the chance of rejecting the lot if it really has 30 defective
chips is:,
3. In the long run, the fraction of lots with 5 defectives that will get
discarded erroneously by this test is:.
4. The smallest number of defectives in the lot for which this test has
at least a 99% chance of correctly detecting that the lot was bad is:.