Chapter 8, Problem 1FDD

Critical Thinking: Testing the Salk Vaccine

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. (Note: The actual Salk vaccine experiment involved another group of 200,745     children who were injected with an ineffective salt solution instead of the Salk vaccine. This study design with a treatment group and     placebo group is very common and very effective. Methods for comparing two proportions are presented in Chapter 9.)

Analyzing the Results

a. Test the given claim using a 0.05 significance level. Does the Salk vaccine appear to be effective?

b. 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 above two errors is a type I error and determine which is a type II error. Which error would have worse consequences? How could the hypothesis test be conducted in order to reduce the chance of making the more serious error?