Question

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 sample size is at least 1000.
B. The requirements are not satisfied; the samples are not simple random samples that are independent.
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 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.

Answer 1

D. 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.

Step-by-step explanation:

Hypothesis Test Requirements: Hypothesis is basically supposing an event before any investigation and then is further investigated to prove the correctness of hypothesis.

So in the given instance we talk about the Salk vaccine for polio under which only 33 developed polio out of a population of 201,229. And that the polio is developed in 115 children in case of placebo vaccine.

The hypothesis of no polio with Salk vaccine is correct.

Here the requirements are fulfilled as there is huge sample and all of them are completely random. Further the results do not depend on any biased event. Also in both cases the favorable and unfavorable event is 5 children at least.