Two consumer labs test the lifetime of a new style of washing machines to see whether they will need service under the warranty before the warranty expires. The company would like a 95% confidence interval for the probability. Lab A tests a sample of nA = 25 washing machines.
They find a probability of failure of pA = 0.12. Lab B takes a different, larger sample of nB = 75 machines. They find a probability of failure of pB = 0.24. The company receives reports from both labs.
a) How should they use the information from the labs?
b) Produce the confidence interval.