In one trip of a cruise ship, 341 of the 3,745 passengers became ill with norovirus. At about the same time 260 of the 1,618 passengers on a second cruise ship also became ill from the norovirus. Treat the sample results as simple random samples from large populations, and use a 0.01 significance level to test the claim that the illness rate on the first ship is less than the rate on the second ship. Based on the result, does it appear that when a norovirus outbreak occurs on a ship, the proportion of infected passengers can vary considerably.