Chapter 6.3, Problem 1Q

Commercial fishermen working certain parts of the Atlantic Ocean sometimes find their efforts hindered by the presence of whales. Ideally, they would like to scare away the whales without frightening the fish. One of the strategies being experimented with is to transmit under-water the sounds of a killer whale. On the fifty-two occasions that technique has been tried, it worked twenty-four times (that is, the whales immediately left the area). Experience has shown, though, that 40% of all whales sighted near fishing boats leave of their own accord, probably just to get away from the noise of the boat.

• (a) Let $p=P$(Whale leaves area after hearing sounds of killer whale). Test $H_0:p=0.40$ versus $H_1:p>0.40$ at the $\alpha =0.05$ level of significance. Can it be argued on the basis of these data that transmitting underwater predator sounds is an effective technique for clearing fishing waters of unwanted whales?

• (b) Calculate the $P$-value for these data. For what values of α would $H_0$ be rejected?