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In a 20202020 survey of 60006000 randomly selected youths ages 1313 to 1717 in the US, 9.5%9.5\% identified as LGBT. Based on the results of the survey, which of the following are reasonable statements?\newlineI.\text{I}. About 9.5%9.5\% of the US population identify as LGBT.\newlineII.\text{II}. About 9.5%9.5\% of youths ages 1313 to 1717 in the US identify as LGBT.\newlineIII.\text{III}. If another 60006000 randomly selected youths ages 1313 to 1717 in the US were surveyed, about 9.5%9.5\% of them would identify as LGBT. \newlineChoose 11 answer:\newline(A) I\text{I} only\newline(B) II\text{II} only\newline(C) I\text{I} and II\text{II} only\newline(D) II\text{II} and III\text{III} only

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Q. In a 20202020 survey of 60006000 randomly selected youths ages 1313 to 1717 in the US, 9.5%9.5\% identified as LGBT. Based on the results of the survey, which of the following are reasonable statements?\newlineI.\text{I}. About 9.5%9.5\% of the US population identify as LGBT.\newlineII.\text{II}. About 9.5%9.5\% of youths ages 1313 to 1717 in the US identify as LGBT.\newlineIII.\text{III}. If another 60006000 randomly selected youths ages 1313 to 1717 in the US were surveyed, about 9.5%9.5\% of them would identify as LGBT. \newlineChoose 11 answer:\newline(A) I\text{I} only\newline(B) II\text{II} only\newline(C) I\text{I} and II\text{II} only\newline(D) II\text{II} and III\text{III} only
  1. Understand Given Information: Understand the given information and what is being asked.\newlineThe survey results show that 9.5%9.5\% of the 60006000 randomly selected youths ages 1313 to 1717 in the US identified as LGBT. We need to determine which statements are reasonable based on this information.
  2. Analyze Statement I: Analyze Statement I: ＂About 9.5%9.5\% of the US population identify as LGBT.＂\newlineThis statement is making a generalization about the entire US population based on a sample of youths ages 1313 to 1717. The sample does not represent the entire population, which includes adults and children of other age groups. Therefore, this statement may not be reasonable.
  3. Analyze Statement II: Analyze Statement II: ＂About 9.5%9.5\% of youths ages 1313 to 1717 in the US identify as LGBT.＂\newlineThis statement is consistent with the survey results, which are based on a sample of youths within the same age range. It is reasonable to say that about 9.5%9.5\% of youths ages 1313 to 1717 in the US identify as LGBT, based on the survey.
  4. Analyze Statement III: Analyze Statement III: ＂If another 60006000 randomly selected youths ages 1313 to 1717 in the US were surveyed, about 9.5%9.5\% of them would identify as LGBT.＂\newlineThis statement assumes that the percentage found in the survey would be the same in another random sample of the same size and demographic. While it is possible that the percentage could be similar, there is no guarantee that exactly 9.5%9.5\% would identify as LGBT in a new survey. Surveys are subject to sampling variability, and the results could be slightly different. Therefore, this statement may not be entirely reasonable.
  5. Choose Correct Answer: Choose the correct answer based on the analysis of the statements.\newlineBased on the analysis, Statement ext{II} is the only one that is reasonable without making broad generalizations or assumptions. Therefore, the correct answer is ( ext{B}) ext{II} only.

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