Question

A new vaccine was recently tested to see if it course 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, 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group.   
Did this study provide significant evidence, at the 5% level, that the vaccination is effective? Do all the steps of a hypothesis test using normal theory methods, including finding a p-value, and write the conclusion in context. Use SE = 0.0107

Check conditions for inference

Does this study provide evidence of causation? Explain why or why not.

Answer 1

The sample proportions here are computed as:
p1 = 333/2455 = 0.1356
p2 = 499/2452 = 0.2035

The test statistic here is computed as:

As this is a one tailed test, the p-value here is computed from the standard normal tables as:
p = P(Z < -6.3458) which is approx. = 0

As the p-value here is negligible or close to 0, the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that the vaccine is effective in clearing the ear infections.