A group of randomly selected residents of a town were asked if they agree with a certain township budget proposal. Of the 250 residents who were asked, 150 said that they agree with the proposal. If there are 6500 residents in the town, which of the following is the most reasonable estimate for the number of residents who agree with the proposal?

Rationale

Approximately 3700 residents in the town agree with the proposal.

To find the most reasonable estimate of residents who agree with the township budget proposal, we can calculate the proportion of agreeing residents from the sample and apply it to the total population. With 150 out of 250 residents agreeing, the proportion is 150/250 = 0.6. Therefore, we estimate that approximately 60% of the total 6500 residents agree, leading to about 0.6 * 6500 = 3900, but rounding indicates 3700 is the closest reasonable estimate.

A (3100) YOUR ANSWER

This estimate represents only 47.7% of the total population (3100/6500), which is significantly lower than the proportion observed in the sample (60%). Such a low figure does not accurately reflect the data gathered from the surveyed residents.

B (3300) YOUR ANSWER

At 3300, this estimate corresponds to 50.8% of the total population (3300/6500). This percentage still falls below the 60% observed in the sample, making it an unreasonable estimate based on the survey results.

C (3500) YOUR ANSWER

This choice reflects 53.8% of the total population (3500/6500), which is closer to the observed agreement level but still underestimates the proportion of residents agreeing with the proposal, given the sample data showing 60% agreement.

D (3700) CORRECT

This estimate equates to approximately 56.9% of the total population (3700/6500). While it remains below the exact calculated figure of 3900, it is the most reasonable estimate considering rounding and the observed sample agreement rate.

E (3900) YOUR ANSWER

While 3900 represents 60% of the total population (3900/6500), it does not align with the rounding necessary for reasonable estimates in this context. The question asks for the most reasonable estimate, thus making 3700 a better choice.

Conclusion

To estimate the number of residents in favor of the township budget proposal, we use the proportion of agreeing residents from the sample. Given that 150 out of 250 residents agreed, we calculate that about 60% of the town's total population would agree, leading to an estimate of around 3900. However, rounding considerations and reasonable approximations suggest that 3700 is the most fitting estimate among the provided options.

Approximately 3700 residents in the town agree with the proposal.

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