To determine how many people must be surveyed to achieve a 75 percent response rate in a city of 6,500 people, you can use the following calculation.
Let \( N \) be the total population (6,500 people), and you want at least 75% of \( N \) to respond.
- Calculate the number of responses needed: \[ 0.75 \times 6500 = 4875 \]
So, you need at least 4,875 responses to meet your goal of a 75% response rate.
- To find out how many people need to be surveyed to get 4,875 responses, you can use the formula for required responses based on the expected response rate.
If \( p \) is the expected response rate (0.75), then the number of people \( n \) that need to be surveyed is given by:
\[ n = \frac{\text{desired responses}}{p} = \frac{4875}{0.75} = 6500 \]
However, this calculation shows how to get responses. Since the goal is generalizable results, if you calculate it the same way:
If you survey 100 people with a 75% response rate, you're expecting 75 responses. Thus, to get the required 4875 responses: \[ n = \frac{4875}{0.75} \approx 6500 \]
This shows to generalize the population while expecting around a 75% response rate, the survey should at least ensure effective contacting to yield these responses.
However for practicality based on given choices, if you currently calculate from responses fitting the choices:
- You should survey 6,500 total to ensure 4,875 responses at 75% rate. But based on options provided, you must note how to count requests as answered more succinctly would gear towards requiring:
The right answer from the choices, thus the only number that connects directly in terms of minimum outputs reaching the generalizability of responses needed is 4,875 people could ideally maximize effectiveness in response ratio.
Therefore, the correct option to ensure the required responses is 4,875 people.
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