Smoke detectors are highly recommended safety devices for early fire detection in homes and businesses. It is vital that the devices be nondefective. Suppose 100 Brand A detectors are tested and 12 fail to emit a warning signal. Subjected to the same test, 15 out of 90 Brand B detectors fail to operate. State the alternative hypothesis that would be used to determine if Brand A has a higher proportion of defective smoke detectors than Brand B. Calculate the test statistic for determining if a difference exists between the failure rates of the two smoke detector brands.