Question: A company is considering a switch to a new supplier for semiconductor chips. It was decided that a switch could take place if evidence were found that the mean number of defects per batch is lower for the new (candidate) supplier than for the old one. It was found that the mean number of defects for 20 batches for the old supplier was 55 with a sample standard deviation of 10 and the mean number of defects for 15 batches for the new supplier is 45 with a sample standard deviation of 12. Is there evidence that the new supplier has lower average defect number at α=0.05? What is the P-value for the test? Make any assumptions you find reasonable.