Question: Another ear infection. In Exercise 13 you used a confidence interval to examine the effectiveness of a vaccine against ear infections in babies. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.)
a) What hypotheses would you test?
b) State a conclusion based on your confidence interval.
c) What alpha level did your test use?
d) If that conclusion is wrong, which type of error did you make?
e) What would be the consequences of such an error?
Exercise: Ear infections. A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did not. During the following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group.
a) Are the conditions for inference satisfied?
b) Find a 95% confidence interval for the difference in rates of ear infection.
c) Use your confidence interval to explain whether you think the vaccine is effective.