In a 2020 survey of 6,000 randomly selected youths ages 13 to 17 in the US, 9.5 percent identified as LGBT. Based on the results of the survey, which of the following are reasonable statements? I. About 9.5 percent of the US population identify as LGBT. II. About 9.5% of youths ages 13 to 17 in the US identify as LGBT. III. If another 6,000 randomly selected youths ages 13 to 17 in the US were surveyed, about 9.5 percent of them would identify as LGBT. Choose 1 answer: (A) I only (B) II only (C) I and II only (D) II and III only

Calculate Percentage: Calculate the percentage of youths who identify as LGBT from the survey. 9.5% of 6,000 = 0.095 * 6,000Perform Multiplication: Perform the multiplication to find the number of youths. 0.095 * 6,000 = 570Statement I: Statement I is about the entire US population, not just youths aged 13 to 17. The survey doesn't provide information about the entire population.Statement II: Statement II is a direct conclusion from the survey results, which is about youths aged 13 to 17 in the US.Statement III: Statement III assumes the same percentage would apply to another survey of 6,000 youths, which might not be true due to variability and sampling differences.

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In a $2020$ survey of $6$ , $000$ randomly selected youths ages $13$ to $17$ in the US, $9$ . $5$ percent identified as LGBT. Based on the results of the survey, which of the following are reasonable statements? $\newline$ I. About $9$ . $5$ percent of the US population identify as LGBT. $\newline$ II. About $9.5 \%$ of youths ages $13$ to $17$ in the US identify as LGBT. $\newline$ III. If another $6$ , $000$ randomly selected youths ages $13$ to $17$ in the US were surveyed, about $9$ . $5$ percent of them would identify as LGBT. $\newline$ Choose $1$ answer: $\newline$ (A) I only $\newline$ (B) II only $\newline$ (C) I and II only $\newline$ (D) II and III only

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Q. In a

2020

survey of

6

000

randomly selected youths ages

13

17

in the US,

9

5

percent identified as LGBT. Based on the results of the survey, which of the following are reasonable statements?

\newline

I. About

9

5

percent of the US population identify as LGBT.

\newline

II. About

9.5 \%

of youths ages

13

17

in the US identify as LGBT.

\newline

III. If another

6

000

randomly selected youths ages

13

17

in the US were surveyed, about

9

5

percent of them would identify as LGBT.

\newline

Choose

1

answer:

\newline

(A) I only

\newline

(B) II only

\newline

\newline

(D) II and III only

Understand given information: Understand the given information. $\newline$ We are given that in a survey of $6,000$ youths ages $13$ to $17$ , $9.5$ percent identified as LGBT. We need to determine which statements are reasonable based on this information.
Evaluate Statement I: Evaluate Statement I. $\newline$ Statement I claims that about $9.5\%$ of the US population identify as LGBT. This statement is making a generalization about the entire US population based on a survey of a specific age group. Without additional information about other age groups, we cannot reasonably extend the survey results to the entire US population.
Evaluate Statement II: Evaluate Statement II. $\newline$ Statement II claims that about $9.5\%$ of youths ages $13$ to $17$ in the US identify as LGBT. This statement is consistent with the survey results, which specifically sampled this age group.
Evaluate Statement III: Evaluate Statement III. $\newline$ Statement III claims that if another $6,000$ randomly selected youths ages $13$ to $17$ in the US were surveyed, about $9.5$ percent of them would identify as LGBT. This statement assumes that the survey results can be replicated exactly in a new sample. While the percentage might be similar, it is not guaranteed to be exactly $9.5$ percent due to the variability inherent in random sampling.
Choose correct answer: Based on the evaluations, Statement II is the only one that is directly supported by the survey results. Statement I is an overgeneralization, and Statement III assumes too much precision in the replication of survey results. Therefore, the correct answer is (B) II only.