**Title: Understanding Requirements for Testing Claims or Constructing Confidence Intervals for Two Population Proportions** **Question:** Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population proportions? **Answer Choices:** A. The sample proportions are from two simple random samples that are independent. B. The sample is at least 5% of the population. C. For each of the two samples, the number of failures is at least 5. D. For each of the two samples, the number of successes is at least 5. --- **Explanation:** When you're testing a claim or constructing a confidence interval estimate for two population proportions, specific requirements must be met to ensure validity. Here, the key is to identify which statement among the choices does not fit these necessary conditions. The provided question and answer choices aim to test your understanding of these requirements. **Detailed Breakdown of Answer Choices:** - **Option A:** "The sample proportions are from two simple random samples that are independent." - This statement is accurate and describes an essential requirement. When comparing two population proportions, the samples must be simple random samples and must be independent of each other. - **Option B:** "The sample is at least 5% of the population." - This is the incorrect statement in the context of this problem. The requirement about sample proportions does not typically state that the sample must be at least 5% of the population. Instead, it usually involves the condition that the sample size is sufficiently large to approximate the population parameter accurately. - **Option C:** "For each of the two samples, the number of failures is at least 5." - This is a valid requirement. To apply the normal approximation when conducting inferences about proportions, it is generally required that both \(np\) and \(n(1-p)\) (i.e., the number of successes and failures, respectively) are at least 5. - **Option D:** "For each of the two samples, the number of successes is at least 5." - This is also correct. Similar to Option C, for the normal approximation to be valid, the number of successes in each sample should be at least 5. By understanding these conditions, students can better grasp the necessary prerequisites for valid statistical testing and confidence interval construction for population proportions.

Title: Understanding Requirements for Testing Claims or Constructing Confidence Intervals for Two Population Proportions Question: Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population proportions? Answer Choices: A. The sample proportions are from two simple random samples that are independent. B. The sample is at least 5% of the population. C. For each of the two samples, the number of failures is at least 5. D. For each of the two samples, the number of successes is at least 5. --- Explanation: When you're testing a claim or constructing a confidence interval estimate for two population proportions, specific requirements must be met to ensure validity. Here, the key is to identify which statement among the choices does not fit these necessary conditions. The provided question and answer choices aim to test your understanding of these requirements. Detailed Breakdown of Answer Choices: - Option A: "The sample proportions are from two simple random samples that are independent." - This statement is accurate and describes an essential requirement. When comparing two population proportions, the samples must be simple random samples and must be independent of each other. - Option B: "The sample is at least 5% of the population." - This is the incorrect statement in the context of this problem. The requirement about sample proportions does not typically state that the sample must be at least 5% of the population. Instead, it usually involves the condition that the sample size is sufficiently large to approximate the population parameter accurately. - Option C: "For each of the two samples, the number of failures is at least 5." - This is a valid requirement. To apply the normal approximation when conducting inferences about proportions, it is generally required that both \(np\) and \(n(1-p)\) (i.e., the number of successes and failures, respectively) are at least 5. - Option D: "For each of the two samples, the number of successes is at least 5." - This is also correct. Similar to Option C, for the normal approximation to be valid, the number of successes in each sample should be at least 5. By understanding these conditions, students can better grasp the necessary prerequisites for valid statistical testing and confidence interval construction for population proportions.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 1GP

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