In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups.

In the largest clinical trial ever​ conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of​ 201,229 children given the Salk vaccine for​ polio, and the other​ 200,745 children were given a placebo. Among those in the treatment​ group, 33 developed​ polio, and among those in the placebo​ group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk​ vaccine, are the requirements for a hypothesis test​ satisfied? Explain.

Choose the correct answer below.

A.

The requirements are​ satisfied; the samples are simple random samples that are​ independent, and for each of the two​ groups, the number of successes is at least 5 and the number of failures is at least 5.

B.

The requirements are​ satisifed; the samples are simple random samples that are​ independent, and for each of the two​ groups, the sample size is at least 1000.

C.

The requirements are not​ satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant.

D.

The requirements are not​ satisfied; the samples are not simple random samples that are independent.