An article described a study that compared flu vaccine administered by injection and flu vaccine administered as a nasal spray. Each of the 8000 children under the age of 5 who participated in the study received both a nasal spray and an injection, but only one was the real vaccine and the other was salt water. At the end of the flu season, it was determined that 3.1% of the 4000 children receiving the real vaccine by nasal spray got sick with the flu and 8.7% of the 4000 receiving the real vaccine by injection got sick with the flu. (a) Why would the researchers give every child both a nasal spray and an injection? It is possible that a patient's knowledge of being given a treatment will itself contribute positively to the health of the patient, so we give them the false perception that they got a treatment when they got none. It is possible that a patient's knowledge of being given one of the treatments will itself contribute positively to the health of the patient, so we want to prevent the patient from knowing which treatment they got. It is possible that being given both treatments will itself contribute positively to the health of the patient, so we give them both. It is possible that a patient's knowledge of being given both treatments will itself contribute positively to the health of the patient, so we give them the perception that they got both. (b) Use the given data to estimate the difference in the proportion of children who get sick with the flu after being vaccinated with an injection and the proportion of children who get sick with the flu after being vaccinated with the nasal spray using a 99% confidence interval. (Use p - Pinjection Pnasal spray* Round your answers to three decimal places.) (c) Based on the confidence interval, would you conclude that the proportion of children who get the flu is different for the two vaccination methods? Zero is not included in the interval. This tells us that we have convincing evidence at the 0.01 confidence level of a difference between the proportion of children who get sick after being vaccinated with an injection and after being vaccinated with the nasal spray. Zero is included in the interval. This tells us that we do not have convincing evidence at the 0.01 confidence level of a difference between the proportion of children who get sick after being vaccinated with an injection and after being vaccinated with the nasal spray. Zero is not included in the interval. This tells us that we do not have convincing evidence at the 0.01 confidence level of a difference between the proportion of children who get sick after being vaccinated with an injection and after being vaccinated with the nasal spray. Zero is included in the interval. This tells us that we have convincing evidence at the 0.01 confidence level of a difference between the proportion of children who get sick after being vaccinated with an injection and after being vaccinated with the nasal spray.