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 not? satisfied; the samples are not simple random samples that are independent. B. 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. C. 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. D. The requirements are not? satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant.

Answer 1

Correct option:

B. 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.

EXPLANATION:

Conditions for two - proportion Z - test:

1. The sampling method for each population is Simple Random Sampling.

2. The samples are independent.

3. Each sample includes at least 5 successes and 5 failures.

4. Each population is at least 10 times as big as its sample.

It is noted that in the given test, all the 5 conditions are satisfied.