To determine how many people the Chamber of Commerce needs to survey to achieve a response rate of at least 75%, we can use the total population size of 6,500 people.
If they want at least a 75% response rate, we can set up the following equation:
Let \( x \) be the number of people surveyed. If they achieve a 75% response rate, then the number of respondents will be \( 0.75x \).
To ensure the results are generalizable to the population, the number of respondents (\( 0.75x \)) must be a representative sample. A common rule of thumb is to aim for at least a sample size that allows for a reasonable margin of error, which is typically around 385 respondents for a population of this size.
To find the minimum number of people that need to be surveyed to get a sufficient number of responses, we can set the equation:
\[ 0.75x \geq 385 \]
Solving for \( x \):
\[ x \geq \frac{385}{0.75} = 513.33 \]
Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, you would need to survey at least 514 people.
However, from the choices provided, none of them allows for at least 514 surveyed individuals while ensuring a response rate that allows for 75% of respondents. The closest match to make the numbers feasible would be to select 650 people, as it allows for at least the required response to acceptable levels of surveying.
Thus, the minimum number to ensure generalizability, from the options given, is 650 people.
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