You have historical quality data for batteries that were randomly assigned to one of 5 groups. Each battery then goes through 3 different quality tests, and each test outcome is binary: pass or fail. Describe a statistically sound way to determine which group has the best overall quality. Your answer should address: - how to define an overall quality metric from the 3 test results; - how to compare the 5 groups even if the sample sizes are different; - how to quantify uncertainty so you do not pick a winner based only on random variation; - how to handle multiple-group comparison when deciding whether one group is truly better than the others.