To determine how many people must be surveyed to achieve a response rate of at least 75% from a population of 6,500, we can set up the calculation as follows:
Let \( x \) be the number of people surveyed. To achieve a 75% response rate, the number of responses needed is:
\[ 0.75x \]
We want this number to be at least 4,875 (which is 75% of 6,500):
\[ 0.75x \geq 4,875 \]
Now, solve for \( x \):
\[ x \geq \frac{4,875}{0.75} \] \[ x \geq 6,500 \]
This means that in order to have at least 4,875 responses, you must survey at least 6,500 people.
Therefore, since the population is only 6,500, surveying the entire population will ensure you get 100% responses, which is more than sufficient for generalizing the results.
From the provided options, none are suitable, as you need to survey 6,500 people to ensure a generalizable result. However, the calculation shows that you cannot achieve the required response rate with any of the listed responses apart from the total population.
The correct answer from given options would be none, based on this calculation. However, if you meant to inquire about any survey below this value at different response rates, that could be evaluated differently.
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