Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.

The study is conducted on 401974 children divided into two groups:

Treatment: of 201229, 33 developed polio.

Placebo: of 200,745, 115 developed polio.

The claim to be tested is whether the rate of polio is less for children in the treatment group or not.

The test of proportions is expected to be conducted.

There are three requirements of the test.

1. Simple random samples: The samples are selected randomly
2. Independence of group: One treatment group considered is 201,229 children given Salk vaccine for polio, and another treatment group of 200,745 children were given Placebo. These two groups are independent of each other, as there is no association between the children in each group.
3. Counts of successes or failures: From each sample, there are at least 5 number of successes and 5 number of failures.

In the treatment group of children, the successes and failures are larger than 5. In Placebo group of children, the successes and failures are larger than 5.

Thus, requirements are satisfied.