Question

The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds 31 in favor of the prison project. What can the city council conclude about public support for the mayor's initiative?

A. The city council can conclude that the city's resonts are not in favor of the prison. While the sample may not be representative and the responses may not be independent, this should not have a significant impact of the estimated proportion
B. The city council can conclude that about 17% of all of the city's residents are in favor of the prison. However, they should also construct a confidence interval to see the range of possible proportions.
C. The city council cannot conclude anything because the residents who showed up for the meeting likely have strong opinions on the matter. Ano, since they are raising their hands, the responses may not be independent
D. The city council can conclude that at least 17% of all of the city's residents are in favor of tho prison. Since the sample largely consisted of disenters, it is safe to assume that mostly people who are against the prison attending the hearing.

Answer 1

The city council cannot conclusively determine public sentiment from the 31 residents in favor out of 183 attendees. The sample may lack representativeness, and raised hands suggest potential bias. Option C is the correct choice.

The city council cannot conclusively infer the overall public sentiment from the small sample of 31 individuals in favor out of 183 residents who attended the meeting. The limitations include potential sample bias and lack of representativeness as those attending may have strong opinions. The observed 17% support may not accurately reflect the entire city's opinion.

Option A is not suitable because it downplays the impact of potential bias and lack of representativeness. Option B overstates the conclusiveness of the observed 17% without considering the need for a confidence interval. Option C is the most reasonable choice as it acknowledges the limitations of the sample's representativeness and the potential for biased responses due to strong opinions.

Therefore, the correct answer is C: "The city council cannot conclude anything because the residents who showed up for the meeting likely have strong opinions on the matter. Also, since they are raising their hands, the responses may not be independent."