At the beginning of World War II, a group of British engineers and statisticians was formed in London to investigate the problem of the lethality of antiaircraft weapons.* One of the main goals of the research team was to assess the probability that a single shell would destroy (or cripple) the aircraft at which it was fired. Although a great deal of data existed at the time on ground-to-ground firing with artillery shells, little information was available on the accuracy of antiaircraft guns. Consequently, a series of trials was run in 1940 in which gun crews shot at free-flying (unpiloted) aircraft. When German aircraft began to bomb England later in that same year, however, the researchers found that the aiming errors of antiaircraft guns under battle stress were considerably greater than those estimated from trials. Let p be the probability that an antiaircraft shell strikes within a 30-foot radius of its target. Assume that under simulated conditions, p = .45.
a. In an actual attack by a single German aircraft, suppose that 3 antiaircraft shells are fired and all 3 miss their target by more than 30 feet. Is it reasonable to conclude that in battle conditions p differs from .45?
b. Answer part a assuming that you observe 10 consecutive shots that all miss their target by more than 30 feet
