The article "Spray Flu Vaccine May Work Better Than Injections for Tots" (San
Luis Obispo Tribune, May 2,2006 ) 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 that 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.
a. Why would the researchers give every child both a nasal spray and an
injection?
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. Based on the confidence
interval, would you conclude that the proportion of children who get the flu
is different for the two vaccination methods?