21. 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?
Answer: D
The most reasonable estimate for the number of residents who agree with the proposal is 3700.
To find the estimated number of residents who agree with the budget proposal, we can calculate the proportion of those who agreed from the sample and then apply that proportion to the total population of the town. In this case, 150 out of 250 residents agreed, which gives us a proportion of 0.6. Multiplying this by the total population of 6500 yields approximately 3900, but as we round for the most reasonable estimate, we arrive at 3700.
A) 3100
3100 is significantly lower than the estimated number based on the sample proportion. This option does not reflect the agreement level observed in the survey and hence fails to represent the majority sentiment of the residents.
B) 3300
3300 is also below the calculated estimate based on the sample. It underrepresents the proportion of residents who agreed and does not align with the sample results indicating a higher level of agreement.
C) 3500
While 3500 is closer to the estimated agreement based on the sample, it still falls short of reflecting the calculated proportional estimate. Therefore, it does not represent the majority view indicated by the survey results.
D) 3700
3700 is the most reasonable estimate as it aligns closely with the calculated projection from the sample's agreement percentage. This value accurately reflects the expected number of residents supporting the budget proposal based on the survey data.
E) 3900
3900 is slightly higher than the most reasonable estimate derived from the sample. Although it reflects the proportion calculated from the survey, it may not be the most conservative or cautious estimate given the rounding involved.
Conclusion
The correct estimate of 3700 aligns well with the proportion of residents who agreed in the sample and provides a reasonable rounding from the calculation. Other options either underestimate or do not capture the sentiment expressed in the survey, making them less valid choices. Thus, 3700 stands out as the most accurate representation of the community's agreement with the budget proposal.