The largest health experiment ever conducted involved a test of the Salk vaccine designed to protect children from the devastating effects of polio. The test included 201,229 children who were given the Salk vaccine, and 33 of them developed polio. The claim that the Salk vaccine is effective is equivalent to the claim that the proportion of vaccinated children who develop polio is less than 0.0000573, which was the rate of polio among children not given the Salk vaccine.
Test the given claim using a 0.05 significance level. Does the Salk vaccine appear to be effective?
For the hypothesis test from part (A), consider the following two errors:
Concluding that the Salk vaccine is effective when it is not effective.
Concluding that the Salk vaccine is not effective when it is effective.
Determine which of the two errors is a Type I error and determine which is a Type II error. Which error would have worse consequences?
A step further
Since our textbook was written prior to 2020, the activity above didnt include the effectiveness of the COVID-19 vaccines. Do some research and find the results of the clinical trials of the different vaccines (Pfizer/Bio-n-Tech, Moderna, and Janssen/Johnson & Johnson) from 2020. What was their effectiveness, and how does this compare with the annual flu vaccine? What are the current death rates of COVID patients who are vaccinated vs unvaccinated? How does this compare with the results of the polio vaccine? What do the data indicate about the possibility of the vaccine eventually eliminating the pandemic?