Consider the following hypothetical example: It is known that the survival rate for a specic disease is p=.85 (or 85%}. Suppose that a researcher wants to test the effectiveness of a new vaccine which is designed to increase the survival rate for patients infected with this disease. If she collects a sample of n=300 vaccinated individuals and finds that 2?0 of them have survived, what can she say about the hypothesis that the vaccine had no effect? She cannot reject the hypothesis that the vaccine had no effect, because the probability of observing 270 or fewer survivors out of a sample of 300 has a probability of 99%, which is much higher than the 5% needed to reject the hypothesis. She cannot reject the hypothesis that the vaccine had no effect, because the probability of observing 2?0 or fewer survivors out of a sample of 300 has a probability of 47% if the hypothesis of an 90% survival rate were true, which is much higher than the 5% needed to reject the hypothesis. She can conclude that there is significant statistical evidence to reject the hypothesis that the vaccine had no effect, because the probability of observing 270 or more survivors out of a sample of 300 would have a probability of less than 5% ifthe hypothesis of an 85% survival rate were true. She can conclude that there is significant statistical evidence to reject the hypothesis that the vaccine had no effect, as 270 is 90% of 300, and the difference between 90% and 85% is 5%, which allows us to reject the hypothesis