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. O A. The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant. OB. 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. OC. 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. OD. The requirements are not satisfied; the samples are not simple random samples that are independent.
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. O A. The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant. OB. 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. OC. 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. OD. The requirements are not satisfied; the samples are not simple random samples that are independent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Clinical Trial for Salk Polio Vaccine: Hypothesis Testing Requirements
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.
---
### Answer Choices
A. **The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant.**
B. **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.**
C. **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.**
D. **The requirements are not satisfied; the samples are not simple random samples that are independent.**
---
### Explanation
This section helps students understand the criteria necessary for conducting a hypothesis test for comparing two population proportions. By analyzing the setup of the clinical trial, we can determine if the tests' requirements are met based on the given data and conditions.
When examining a hypothesis test involving two population proportions, one must ensure that:
1. The samples are simple random samples.
2. The samples are independent.
3. The sample sizes are sufficiently large, often at least 5 successes and 5 failures, or sometimes at least 1000 participants in each group.
For this specific case, students are encouraged to critically analyze the provided data and select the appropriate answer accordingly.
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