The quality control department of Widgets Manufacturing needs your help. They can't decide which significance level is appropriate for testing the claim that fewer than 50% of widgets from a production run are defective. One group feels that the primary consideration for choosing between alpha=0.01 and alpha=0.05 should be to keep the rejection rate of good widgets as small as possible, while the other group feels they should try to keep the number of defective widgets that make it through to a minimum. Write two paragraphs detailing the arguments might each group make to support their position. Your paragraphs should include the terms alternative hypothesis, Type I error, Type II error, and sample size. Which significance level would you choose? In a sample of 1500 widgets it is found that 679 are defective. Test the claim at the significance level you chose and state your conclusion in non-technical terms. Make sure to show all the steps of the hypothesis testing.