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 3.9% of the 4000 children receiving the real vaccine by nasal spray got sick with the flu and 8.6% of the 4000 receiving the real vaccine by injection got sick with the flu.

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 μinjection − μnasal spray. Round your answers to three decimal places.)